34:I[651451,["/_next/static/chunks/0g36cb-mcivw7.js?dpl=nogit-1790701396","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1790701396","/_next/static/chunks/2zbd126_oyq__.js?dpl=nogit-1790701396","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790701396","/_next/static/chunks/15le0xz0fig32.js?dpl=nogit-1790701396","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790701396","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790701396","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790701396","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790701396","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790701396","/_next/static/chunks/1bsq1mchpwo6z.js?dpl=nogit-1790701396","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790701396","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790701396","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790701396","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790701396","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790701396","/_next/static/chunks/2bsb8adax1pdp.js?dpl=nogit-1790701396","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790701396","/_next/static/chunks/2u46tugibrk1v.js?dpl=nogit-1790701396","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790701396","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790701396","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790701396","/_next/static/chunks/3_lt5xft2vli-.js?dpl=nogit-1790701396","/_next/static/chunks/309o1kfcg2jbm.js?dpl=nogit-1790701396","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790701396","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790701396","/_next/static/chunks/3t0ml5lpxv0ny.js?dpl=nogit-1790701396","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790701396","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790701396","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790701396","/_next/static/chunks/01yo0wxu33311.js?dpl=nogit-1790701396","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790701396","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790701396","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790701396","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790701396","/_next/static/chunks/00ttxm70xm75x.js?dpl=nogit-1790701396","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790701396","/_next/static/chunks/375u4k1enjdjk.js?dpl=nogit-1790701396","/_next/static/chunks/2nhkb7qo19pt9.js?dpl=nogit-1790701396","/_next/static/chunks/1r90gnkk5yun0.js?dpl=nogit-1790701396","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790701396","/_next/static/chunks/0i4zom-kyjeci.js?dpl=nogit-1790701396","/_next/static/chunks/181u0pe6-1__x.js?dpl=nogit-1790701396","/_next/static/chunks/1h-hlqpew4bkg.js?dpl=nogit-1790701396","/_next/static/chunks/2opkuzmjw8cxb.js?dpl=nogit-1790701396","/_next/static/chunks/3-zx6jlroq8f_.js?dpl=nogit-1790701396","/_next/static/chunks/0m6ugdwrai1f_.js?dpl=nogit-1790701396","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790701396","/_next/static/chunks/2job6vzx9q1be.js?dpl=nogit-1790701396","/_next/static/chunks/10u-zuc7e4u51.js?dpl=nogit-1790701396","/_next/static/chunks/12lt_672t_i5k.js?dpl=nogit-1790701396","/_next/static/chunks/2olvbq0sf9-5z.js?dpl=nogit-1790701396","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790701396","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790701396","/_next/static/chunks/0f-6p5pag2tjw.js?dpl=nogit-1790701396","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790701396","/_next/static/chunks/27300xkio5zct.js?dpl=nogit-1790701396","/_next/static/chunks/27wr6uo36_o7k.js?dpl=nogit-1790701396","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790701396","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790701396","/_next/static/chunks/1jf3y60i704h7.js?dpl=nogit-1790701396","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790701396","/_next/static/chunks/237j9p1936g2m.js?dpl=nogit-1790701396","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790701396"],"UserProgressProvider"] 35:I[196793,["/_next/static/chunks/0g36cb-mcivw7.js?dpl=nogit-1790701396","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1790701396","/_next/static/chunks/2zbd126_oyq__.js?dpl=nogit-1790701396","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790701396","/_next/static/chunks/15le0xz0fig32.js?dpl=nogit-1790701396","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790701396","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790701396","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790701396","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790701396","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790701396","/_next/static/chunks/1bsq1mchpwo6z.js?dpl=nogit-1790701396","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790701396","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790701396","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790701396","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790701396","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790701396","/_next/static/chunks/2bsb8adax1pdp.js?dpl=nogit-1790701396","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790701396","/_next/static/chunks/2u46tugibrk1v.js?dpl=nogit-1790701396","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790701396","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790701396","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790701396","/_next/static/chunks/3_lt5xft2vli-.js?dpl=nogit-1790701396","/_next/static/chunks/309o1kfcg2jbm.js?dpl=nogit-1790701396","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790701396","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790701396","/_next/static/chunks/3t0ml5lpxv0ny.js?dpl=nogit-1790701396","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790701396","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790701396","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790701396","/_next/static/chunks/01yo0wxu33311.js?dpl=nogit-1790701396","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790701396","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790701396","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790701396","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790701396","/_next/static/chunks/00ttxm70xm75x.js?dpl=nogit-1790701396","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790701396","/_next/static/chunks/375u4k1enjdjk.js?dpl=nogit-1790701396","/_next/static/chunks/2nhkb7qo19pt9.js?dpl=nogit-1790701396","/_next/static/chunks/1r90gnkk5yun0.js?dpl=nogit-1790701396","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790701396","/_next/static/chunks/0i4zom-kyjeci.js?dpl=nogit-1790701396","/_next/static/chunks/181u0pe6-1__x.js?dpl=nogit-1790701396","/_next/static/chunks/1h-hlqpew4bkg.js?dpl=nogit-1790701396","/_next/static/chunks/2opkuzmjw8cxb.js?dpl=nogit-1790701396","/_next/static/chunks/3-zx6jlroq8f_.js?dpl=nogit-1790701396","/_next/static/chunks/0m6ugdwrai1f_.js?dpl=nogit-1790701396","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790701396","/_next/static/chunks/2job6vzx9q1be.js?dpl=nogit-1790701396","/_next/static/chunks/10u-zuc7e4u51.js?dpl=nogit-1790701396","/_next/static/chunks/12lt_672t_i5k.js?dpl=nogit-1790701396","/_next/static/chunks/2olvbq0sf9-5z.js?dpl=nogit-1790701396","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790701396","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790701396","/_next/static/chunks/0f-6p5pag2tjw.js?dpl=nogit-1790701396","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790701396","/_next/static/chunks/27300xkio5zct.js?dpl=nogit-1790701396","/_next/static/chunks/27wr6uo36_o7k.js?dpl=nogit-1790701396","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790701396","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790701396","/_next/static/chunks/1jf3y60i704h7.js?dpl=nogit-1790701396","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790701396","/_next/static/chunks/237j9p1936g2m.js?dpl=nogit-1790701396","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790701396"],"Gingerbread"] 37:I[716297,["/_next/static/chunks/0g36cb-mcivw7.js?dpl=nogit-1790701396","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1790701396","/_next/static/chunks/2zbd126_oyq__.js?dpl=nogit-1790701396","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790701396","/_next/static/chunks/15le0xz0fig32.js?dpl=nogit-1790701396","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790701396","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790701396","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790701396","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790701396","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790701396","/_next/static/chunks/1bsq1mchpwo6z.js?dpl=nogit-1790701396","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790701396","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790701396","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790701396","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790701396","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790701396","/_next/static/chunks/2bsb8adax1pdp.js?dpl=nogit-1790701396","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790701396","/_next/static/chunks/2u46tugibrk1v.js?dpl=nogit-1790701396","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790701396","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790701396","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790701396","/_next/static/chunks/3_lt5xft2vli-.js?dpl=nogit-1790701396","/_next/static/chunks/309o1kfcg2jbm.js?dpl=nogit-1790701396","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790701396","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790701396","/_next/static/chunks/3t0ml5lpxv0ny.js?dpl=nogit-1790701396","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790701396","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790701396","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790701396","/_next/static/chunks/01yo0wxu33311.js?dpl=nogit-1790701396","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790701396","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790701396","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790701396","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790701396","/_next/static/chunks/00ttxm70xm75x.js?dpl=nogit-1790701396","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790701396","/_next/static/chunks/375u4k1enjdjk.js?dpl=nogit-1790701396","/_next/static/chunks/2nhkb7qo19pt9.js?dpl=nogit-1790701396","/_next/static/chunks/1r90gnkk5yun0.js?dpl=nogit-1790701396","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790701396","/_next/static/chunks/0i4zom-kyjeci.js?dpl=nogit-1790701396","/_next/static/chunks/181u0pe6-1__x.js?dpl=nogit-1790701396","/_next/static/chunks/1h-hlqpew4bkg.js?dpl=nogit-1790701396","/_next/static/chunks/2opkuzmjw8cxb.js?dpl=nogit-1790701396","/_next/static/chunks/3-zx6jlroq8f_.js?dpl=nogit-1790701396","/_next/static/chunks/0m6ugdwrai1f_.js?dpl=nogit-1790701396","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790701396","/_next/static/chunks/2job6vzx9q1be.js?dpl=nogit-1790701396","/_next/static/chunks/10u-zuc7e4u51.js?dpl=nogit-1790701396","/_next/static/chunks/12lt_672t_i5k.js?dpl=nogit-1790701396","/_next/static/chunks/2olvbq0sf9-5z.js?dpl=nogit-1790701396","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790701396","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790701396","/_next/static/chunks/0f-6p5pag2tjw.js?dpl=nogit-1790701396","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790701396","/_next/static/chunks/27300xkio5zct.js?dpl=nogit-1790701396","/_next/static/chunks/27wr6uo36_o7k.js?dpl=nogit-1790701396","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790701396","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790701396","/_next/static/chunks/1jf3y60i704h7.js?dpl=nogit-1790701396","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790701396","/_next/static/chunks/237j9p1936g2m.js?dpl=nogit-1790701396","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790701396"],"TopicRecentlyViewed"] 38:I[647935,["/_next/static/chunks/0g36cb-mcivw7.js?dpl=nogit-1790701396","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1790701396","/_next/static/chunks/2zbd126_oyq__.js?dpl=nogit-1790701396","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790701396","/_next/static/chunks/15le0xz0fig32.js?dpl=nogit-1790701396","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790701396","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790701396","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790701396","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790701396","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790701396","/_next/static/chunks/1bsq1mchpwo6z.js?dpl=nogit-1790701396","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790701396","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790701396","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790701396","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790701396","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790701396","/_next/static/chunks/2bsb8adax1pdp.js?dpl=nogit-1790701396","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790701396","/_next/static/chunks/2u46tugibrk1v.js?dpl=nogit-1790701396","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790701396","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790701396","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790701396","/_next/static/chunks/3_lt5xft2vli-.js?dpl=nogit-1790701396","/_next/static/chunks/309o1kfcg2jbm.js?dpl=nogit-1790701396","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790701396","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790701396","/_next/static/chunks/3t0ml5lpxv0ny.js?dpl=nogit-1790701396","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790701396","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790701396","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790701396","/_next/static/chunks/01yo0wxu33311.js?dpl=nogit-1790701396","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790701396","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790701396","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790701396","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790701396","/_next/static/chunks/00ttxm70xm75x.js?dpl=nogit-1790701396","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790701396","/_next/static/chunks/375u4k1enjdjk.js?dpl=nogit-1790701396","/_next/static/chunks/2nhkb7qo19pt9.js?dpl=nogit-1790701396","/_next/static/chunks/1r90gnkk5yun0.js?dpl=nogit-1790701396","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790701396","/_next/static/chunks/0i4zom-kyjeci.js?dpl=nogit-1790701396","/_next/static/chunks/181u0pe6-1__x.js?dpl=nogit-1790701396","/_next/static/chunks/1h-hlqpew4bkg.js?dpl=nogit-1790701396","/_next/static/chunks/2opkuzmjw8cxb.js?dpl=nogit-1790701396","/_next/static/chunks/3-zx6jlroq8f_.js?dpl=nogit-1790701396","/_next/static/chunks/0m6ugdwrai1f_.js?dpl=nogit-1790701396","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790701396","/_next/static/chunks/2job6vzx9q1be.js?dpl=nogit-1790701396","/_next/static/chunks/10u-zuc7e4u51.js?dpl=nogit-1790701396","/_next/static/chunks/12lt_672t_i5k.js?dpl=nogit-1790701396","/_next/static/chunks/2olvbq0sf9-5z.js?dpl=nogit-1790701396","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790701396","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790701396","/_next/static/chunks/0f-6p5pag2tjw.js?dpl=nogit-1790701396","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790701396","/_next/static/chunks/27300xkio5zct.js?dpl=nogit-1790701396","/_next/static/chunks/27wr6uo36_o7k.js?dpl=nogit-1790701396","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790701396","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790701396","/_next/static/chunks/1jf3y60i704h7.js?dpl=nogit-1790701396","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790701396","/_next/static/chunks/237j9p1936g2m.js?dpl=nogit-1790701396","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790701396"],"RecordResourceResume"] 39:I[426249,["/_next/static/chunks/0g36cb-mcivw7.js?dpl=nogit-1790701396","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1790701396","/_next/static/chunks/2zbd126_oyq__.js?dpl=nogit-1790701396","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790701396","/_next/static/chunks/15le0xz0fig32.js?dpl=nogit-1790701396","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790701396","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790701396","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790701396","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790701396","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790701396","/_next/static/chunks/1bsq1mchpwo6z.js?dpl=nogit-1790701396","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790701396","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790701396","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790701396","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790701396","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790701396","/_next/static/chunks/2bsb8adax1pdp.js?dpl=nogit-1790701396","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790701396","/_next/static/chunks/2u46tugibrk1v.js?dpl=nogit-1790701396","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790701396","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790701396","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790701396","/_next/static/chunks/3_lt5xft2vli-.js?dpl=nogit-1790701396","/_next/static/chunks/309o1kfcg2jbm.js?dpl=nogit-1790701396","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790701396","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790701396","/_next/static/chunks/3t0ml5lpxv0ny.js?dpl=nogit-1790701396","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790701396","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790701396","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790701396","/_next/static/chunks/01yo0wxu33311.js?dpl=nogit-1790701396","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790701396","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790701396","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790701396","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790701396","/_next/static/chunks/00ttxm70xm75x.js?dpl=nogit-1790701396","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790701396","/_next/static/chunks/375u4k1enjdjk.js?dpl=nogit-1790701396","/_next/static/chunks/2nhkb7qo19pt9.js?dpl=nogit-1790701396","/_next/static/chunks/1r90gnkk5yun0.js?dpl=nogit-1790701396","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790701396","/_next/static/chunks/0i4zom-kyjeci.js?dpl=nogit-1790701396","/_next/static/chunks/181u0pe6-1__x.js?dpl=nogit-1790701396","/_next/static/chunks/1h-hlqpew4bkg.js?dpl=nogit-1790701396","/_next/static/chunks/2opkuzmjw8cxb.js?dpl=nogit-1790701396","/_next/static/chunks/3-zx6jlroq8f_.js?dpl=nogit-1790701396","/_next/static/chunks/0m6ugdwrai1f_.js?dpl=nogit-1790701396","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790701396","/_next/static/chunks/2job6vzx9q1be.js?dpl=nogit-1790701396","/_next/static/chunks/10u-zuc7e4u51.js?dpl=nogit-1790701396","/_next/static/chunks/12lt_672t_i5k.js?dpl=nogit-1790701396","/_next/static/chunks/2olvbq0sf9-5z.js?dpl=nogit-1790701396","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790701396","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790701396","/_next/static/chunks/0f-6p5pag2tjw.js?dpl=nogit-1790701396","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790701396","/_next/static/chunks/27300xkio5zct.js?dpl=nogit-1790701396","/_next/static/chunks/27wr6uo36_o7k.js?dpl=nogit-1790701396","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790701396","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790701396","/_next/static/chunks/1jf3y60i704h7.js?dpl=nogit-1790701396","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790701396","/_next/static/chunks/237j9p1936g2m.js?dpl=nogit-1790701396","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790701396"],"TopicQuestionBank"] 25:["$","$L34",null,{"bundle":{"topicIds":["43b3ff0e-f970-fc63-7b68-b72092e4b3a4"],"paperIds":[],"stageIds":[],"stageTopicIds":[],"stageAssessmentIds":[],"topicNoteIds":["5ee85874-bda7-4363-28a0-c5edcd065e51"]},"children":[["$","$L35",null,{"feature":"question-bank"}],"$L36",["$","$L37",null,{"subjectCode":"gcse_maths__wjec","subjectName":"Maths","topicSlug":"grade-3-3-15-drawing-linear-graphs","topicTitle":"Drawing Linear Graphs","sectionTitle":null,"activity":"worksheet","resourceTitle":"Drawing Linear Graphs Questions","resourceHref":"/gcse/maths/wjec/grade-3-3-15-drawing-linear-graphs/questions/q1","saveTrail":false}],["$","$L38",null,{"href":"/gcse/maths/wjec/grade-3-3-15-drawing-linear-graphs/questions/q1","label":"Drawing Linear Graphs","subjectCode":"gcse_maths__wjec","surface":"questions"}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"LearningResource\",\"name\":\"Question 21 – Drawing Linear Graphs - GCSE Maths Questions\",\"description\":\"Practise Drawing Linear Graphs GCSE Maths exam-style questions with worked solutions on MathsGenie.\",\"learningResourceType\":\"Practice questions\",\"educationalLevel\":\"GCSE\",\"about\":{\"@type\":\"Thing\",\"name\":\"Drawing Linear Graphs\"},\"url\":\"https://mathsgenie.co.uk/gcse/maths/wjec/grade-3-3-15-drawing-linear-graphs/questions/q21\",\"inLanguage\":\"en-GB\",\"provider\":{\"@id\":\"https://mathsgenie.co.uk/#organization\"}}"}}],["$","div",null,{"className":"min-h-0 w-full flex-1 overflow-hidden bg-background","children":["$","$L39",null,{"backHref":"/gcse/maths/wjec/questions","basePath":"/gcse/maths/wjec/grade-3-3-15-drawing-linear-graphs/questions","formulaUrl":null,"initialIndex":20,"initialQuestionWindow":[{"id":"c2e9d857-8335-4e2d-9b9a-ec1305ec204c","revisionId":"befc6327-2512-4c9f-acc2-aabf9e8965ff","questionNumber":null,"questionType":"LA","specification":"","difficultyBand":"easy","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":false,"parts":[{"id":"c59e67ca-4f37-498e-a19d-1f3cc0b18f02","label":"a","content":"Complete the table of values for $y = 2x + 3$\n\n| $x$ | -2 | -1 | 0 | 1 | 2 | 3 |\n|-----|----|----|---|---|---|---|\n| $y$ | | | | | | |","markscheme":"- Correct values in table: -1, 1, 3, 5, 7, 9 B2\n- Award 1 mark for 2 or 3 correct values B1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Award 1 mark for 2 or 3 correct values.","code":"B"},{"id":"p2","marks":1,"description":"Award 2nd mark for all 6 correct values (-1, 1, 3, 5, 7, 9).","code":"B"}],"finalAnswers":["-1, 1, 3, 5, 7, 9"],"generatedAt":"2026-05-06T14:00:07.988Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"substitution","label":"Substitute each x-value","steps":[{"type":"text","order":0,"title":"Use the formula","content":"For each column, replace $x$ in $y=2x+3$ with the $x$-value at the top of that column. Keep brackets around a negative value so its sign is clear.","highlights":[{"text":"Complete the table of values for $y = 2x + 3$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x=-2:\\quad 2(-2)+3\\;\\longmapsto\\;\\htmlData{anchor=r1}{\\color{@sky}{-1}}$"},{"latex":"$$x=-1:\\quad 2(-1)+3\\;\\longmapsto\\;\\htmlData{anchor=r2}{\\color{@sky}{1}}$"},{"latex":"$$x=0:\\quad 2(0)+3\\;\\longmapsto\\;\\htmlData{anchor=r3}{\\color{@sky}{3}}$"},{"latex":"$$x=1:\\quad 2(1)+3\\;\\longmapsto\\;\\htmlData{anchor=r4}{\\color{@green}{5}}$"},{"latex":"$$x=2:\\quad 2(2)+3\\;\\longmapsto\\;\\htmlData{anchor=r5}{\\color{@green}{7}}$"},{"latex":"$$x=3:\\quad 2(3)+3\\;\\longmapsto\\;\\htmlData{anchor=r6}{\\color{@green}{9}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"r1"},{"color":"sky","style":"text-color","anchor":"r2"},{"color":"sky","style":"text-color","anchor":"r3"},{"color":"green","style":"text-color","anchor":"r4"},{"color":"green","style":"text-color","anchor":"r5"},{"color":"green","style":"text-color","anchor":"r6"}]},"order":1,"title":"Calculate each value","description":"Substitute each value of x. Multiply by 2, then add 3; brackets keep negative values clear."},{"type":"text","order":2,"title":"Complete the table","content":"Enter the values in the same order as their corresponding $x$-values:\n\n| $x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ |\n|---|---:|---:|---:|---:|---:|---:|\n| $y$ | $-1$ | $1$ | $3$ | $5$ | $7$ | $9$ |\n\nAll six correct values earn **2 marks**. If only two or three values are correct, this earns **1 mark**.","highlights":[{"text":"Complete the table of values for $y = 2x + 3$","location":"specification"}]}]}],"generatedAt":"2026-07-19T15:57:00.502Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"bffe73cc-0227-4638-be2b-2605368696dd","label":"b","content":"On the grid, draw the graph of $y = 2x + 3$ for values of $x$ from -2 to 3\n\n![A coordinate grid for drawing the graph of y = 2x + 3.](https://assets.mathsgenie.co.uk/figures/coords/47e754182c4b500d72fffc380c485a826118d845e475186c0bbbe3e04c34eff1.png)","markscheme":"- Points plotted correctly from table M1\n- Correct straight line drawn from $x = -2$ to $x = 3$ A1\n\n![Solution](https://assets.mathsgenie.co.uk/figures/coords/499ea76771f37ff40f454e74da2c5e5688083de65c390f312a1d796fd872011b.png)","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Points from the table plotted correctly (allow follow-through from incorrect table values).","code":"M"},{"id":"p2","marks":1,"description":"A single straight line correctly drawn for the range x = -2 to x = 3.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-06T14:00:07.988Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"table_then_line","label":"Make a table, then draw","steps":[{"type":"text","order":0,"title":"Choose the x-values","content":"Use each whole-number value of $x$ from $-2$ to $3$. For every value, substitute it into $y=2x+3$ to find the matching $y$-coordinate.","highlights":[{"text":"for values of $x$ from -2 to 3","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\color{@sky}{\\htmlData{anchor=table}{\\begin{array}{c|rrrrrr}x&-2&-1&0&1&2&3\\\\ \\hline y=2x+3&-1&1&3&5&7&9\\end{array}}}$"},{"latex":"$$\\color{@green}{\\htmlData{anchor=pairs}{(-2,-1),\\ (-1,1),\\ (0,3),\\ (1,5),\\ (2,7),\\ (3,9)}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"table"},{"color":"green","style":"text-color","anchor":"pairs"}],"connections":[{"to":"pairs","from":"table","color":"teal","label":"read down each column"}]},"order":1,"title":"Calculate the coordinates","description":"Multiply each input by two, then add three. Read each column as one coordinate pair."},{"type":"graph","order":2,"title":"Plot the points","viewport":{"top":10,"left":-3,"right":4,"bottom":-2},"axisLabels":{"x":"x","y":"y"},"description":"Plot all six coordinates from the table. Their correct positions earn M1.","expressions":[{"id":"expr-0","color":"sky","latex":"(-2,-1)","pointStyle":"point"},{"id":"expr-1","color":"sky","latex":"(-1,1)","pointStyle":"point"},{"id":"expr-2","color":"sky","latex":"(0,3)","pointStyle":"point"},{"id":"expr-3","color":"sky","latex":"(1,5)","pointStyle":"point"},{"id":"expr-4","color":"sky","latex":"(2,7)","pointStyle":"point"},{"id":"expr-5","color":"sky","latex":"(3,9)","pointStyle":"point"}]},{"type":"graph","order":3,"title":"Join with a ruler","viewport":{"top":10,"left":-3,"right":4,"bottom":-2},"axisLabels":{"x":"x","y":"y"},"description":"Use a ruler to draw one straight line segment through the plotted points. Stop at the two endpoints because the stated range is from x = -2 to x = 3. This correct line earns A1.","expressions":[{"id":"expr-0","color":"green","latex":"y=2x+3\\left\\{-2\\le x\\le3\\right\\}"},{"id":"expr-1","color":"green","label":"(-2, -1)","latex":"(-2,-1)","labelOrientation":"below"},{"id":"expr-2","color":"green","latex":"(-1,1)"},{"id":"expr-3","color":"green","latex":"(0,3)"},{"id":"expr-4","color":"green","latex":"(1,5)"},{"id":"expr-5","color":"green","latex":"(2,7)"},{"id":"expr-6","color":"green","label":"(3, 9)","latex":"(3,9)","labelOrientation":"above"},{"id":"expr-7","color":"green","label":"y = 2x + 3","latex":"(1.5,6)","hidden":true,"labelOrientation":"above"}]}]}],"generatedAt":"2026-07-19T16:02:55.769Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"c59e67ca-4f37-498e-a19d-1f3cc0b18f02:substitution","label":"(a) Direct Substitution","steps":[{"type":"text","order":0,"title":"Understand the goal","content":"We need to find the missing $y$-values for the equation $y = 2x + 3$ by substituting each given $x$-value from the table into the equation."},{"type":"hyper_latex","block":{"nodes":[{"text":"Let's substitute the negative $x$-values, $x = -2$ and $x = -1$:"},{"latex":"$$$\n\\begin{aligned}\n\\text{For } \\htmlData{anchor=x1}{\\color{@sky}{x = -2}}:\\quad y &= 2(\\htmlData{anchor=sub1}{\\color{@sky}{-2}}) + 3 \\\\\n&= -4 + 3 \\\\\n&= \\htmlData{anchor=y1}{\\color{@pink}{-1}}\n\\end{aligned}\n$$"},{"latex":"$$$\n\\begin{aligned}\n\\text{For } \\htmlData{anchor=x2}{\\color{@purple}{x = -1}}:\\quad y &= 2(\\htmlData{anchor=sub2}{\\color{@purple}{-1}}) + 3 \\\\\n&= -2 + 3 \\\\\n&= \\htmlData{anchor=y2}{\\color{@orange}{1}}\n\\end{aligned}\n$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"x1"},{"color":"pink","style":"box","anchor":"y1"},{"color":"purple","style":"text-color","anchor":"x2"},{"color":"orange","style":"box","anchor":"y2"}],"connections":[{"to":"sub1","from":"x1","color":"sky","label":"substitute","style":"solid"},{"to":"sub2","from":"x2","color":"purple","label":"substitute","style":"solid"}]},"order":1,"title":"Substitute negative values","description":"We replace $x$ with $-2$ and $-1$ to get the first two $y$-values."},{"type":"hyper_latex","block":{"nodes":[{"text":"Now, substitute $x = 0$ and $x = 1$:"},{"latex":"$$$\n\\begin{aligned}\n\\text{For } \\htmlData{anchor=x3}{\\color{@green}{x = 0}}:\\quad y &= 2(\\htmlData{anchor=sub3}{\\color{@green}{0}}) + 3 \\\\\n&= 0 + 3 \\\\\n&= \\htmlData{anchor=y3}{\\color{@teal}{3}}\n\\end{aligned}\n$$"},{"latex":"$$$\n\\begin{aligned}\n\\text{For } \\htmlData{anchor=x4}{\\color{@amber}{x = 1}}:\\quad y &= 2(\\htmlData{anchor=sub4}{\\color{@amber}{1}}) + 3 \\\\\n&= 2 + 3 \\\\\n&= \\htmlData{anchor=y4}{\\color{@red}{5}}\n\\end{aligned}\n$$"}],"highlights":[{"color":"green","style":"text-color","anchor":"x3"},{"color":"teal","style":"box","anchor":"y3"},{"color":"amber","style":"text-color","anchor":"x4"},{"color":"red","style":"box","anchor":"y4"}],"connections":[{"to":"sub3","from":"x3","color":"green","label":"substitute","style":"solid"},{"to":"sub4","from":"x4","color":"amber","label":"substitute","style":"solid"}]},"order":2,"title":"Substitute middle values","description":"Substitute $0$ and $1$ to find the next two values."},{"type":"hyper_latex","block":{"nodes":[{"text":"Finally, substitute $x = 2$ and $x = 3$:"},{"latex":"$$$\n\\begin{aligned}\n\\text{For } \\htmlData{anchor=x5}{\\color{@indigo}{x = 2}}:\\quad y &= 2(\\htmlData{anchor=sub5}{\\color{@indigo}{2}}) + 3 \\\\\n&= 4 + 3 \\\\\n&= \\htmlData{anchor=y5}{\\color{@pink}{7}}\n\\end{aligned}\n$$"},{"latex":"$$$\n\\begin{aligned}\n\\text{For } \\htmlData{anchor=x6}{\\color{@teal}{x = 3}}:\\quad y &= 2(\\htmlData{anchor=sub6}{\\color{@teal}{3}}) + 3 \\\\\n&= 6 + 3 \\\\\n&= \\htmlData{anchor=y6}{\\color{@orange}{9}}\n\\end{aligned}\n$$"}],"highlights":[{"color":"indigo","style":"text-color","anchor":"x5"},{"color":"pink","style":"box","anchor":"y5"},{"color":"teal","style":"text-color","anchor":"x6"},{"color":"orange","style":"box","anchor":"y6"}],"connections":[{"to":"sub5","from":"x5","color":"indigo","label":"substitute","style":"solid"},{"to":"sub6","from":"x6","color":"teal","label":"substitute","style":"solid"}]},"order":3,"title":"Substitute remaining values","description":"Substitute $2$ and $3$ to complete the remaining columns."},{"type":"text","order":4,"title":"Complete the table","content":"Now we can write down the complete table of values:\n\n| $x$ | -2 | -1 | 0 | 1 | 2 | 3 |\n|---|---|---|---|---|---|---|\n| $y$ | **-1** | **1** | **3** | **5** | **7** | **9** |\n\nAll six values match the expected markscheme answer."}]},{"id":"c59e67ca-4f37-498e-a19d-1f3cc0b18f02:pattern","label":"(a) Linear Pattern Recognition","steps":[{"type":"text","order":0,"title":"Understand the linear pattern","content":"The equation we are working with is:\n\n$$y = 2x + 3$$\n\nThis is a linear equation in the form $y = mx + c$, where the gradient is $m = 2$. \n\nBecause the gradient is $2$, it means that every time $x$ increases by $1$, the value of $y$ will increase by exactly $2$ (a constant difference of $2$). We can use this linear pattern to quickly complete the table once we find a couple of starting points."},{"type":"hyper_latex","block":{"nodes":[{"text":"Let's find the value of $y$ when $x = 0$ by substituting it into the equation:"},{"latex":"$$y = 2(\\htmlData{anchor=x-zero}{\\color{@sky}{0}}) + 3 = \\htmlData{anchor=y-three}{\\color{@sky}{3}}$"},{"text":"Now, let's find the value when $x = 1$:"},{"latex":"$$y = 2(\\htmlData{anchor=x-one}{\\color{@amber}{1}}) + 3 = 2 + 3 = \\htmlData{anchor=y-five}{\\color{@amber}{5}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"x-zero"},{"color":"sky","style":"text-color","anchor":"y-three"},{"color":"amber","style":"text-color","anchor":"x-one"},{"color":"amber","style":"text-color","anchor":"y-five"}],"connections":[{"to":"y-three","from":"x-zero","color":"sky","label":"when x=0","style":"solid"},{"to":"y-five","from":"x-one","color":"amber","label":"when x=1","style":"solid"}]},"order":1,"title":"Find the starting values","description":"We start by calculating the values at easy integer points like $x = 0$ and $x = 1$ to establish our starting values."},{"type":"text","order":2,"title":"Apply the pattern moving forward","content":"Since we know $y = 3$ when $x = 0$ and $y = 5$ when $x = 1$, we can see the constant difference of $+2$ in action:\n\n$$3 \\xrightarrow{+2} 5$$\n\nLet's continue adding $2$ to find the remaining values for $x = 2$ and $x = 3$:\n\n* For $x = 2$: \n $$5 + 2 = 7$$\n* For $x = 3$: \n $$7 + 2 = 9$$"},{"type":"text","order":3,"title":"Apply the pattern moving backward","content":"To find the values for the negative $x$ values, we work backwards from $x = 0$ by subtracting $2$ for each step to the left:\n\n* For $x = -1$: \n $$3 - 2 = 1$$\n* For $x = -2$: \n $$1 - 2 = -1$$"},{"type":"text","order":4,"title":"Complete the table","content":"Now we can write down the fully completed table:\n\n| $x$ | -2 | -1 | 0 | 1 | 2 | 3 |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: |\n| $y$ | **-1** | **1** | **3** | **5** | **7** | **9** |\n\nEach $y$-value increases by $2$ sequentially, confirming our linear pattern recognition method is correct."}]},{"id":"c59e67ca-4f37-498e-a19d-1f3cc0b18f02:calculator","label":"(a) Calculator Table Mode","steps":[{"type":"text","order":0,"title":"Identify the goal","content":"We need to find the corresponding $y$-values for the given $x$-values (from $-2$ to $3$) using the linear equation:\n\n$$y = 2x + 3$$\n\nTo do this quickly and accurately, we can use the **Table** function on a scientific calculator.","highlights":[{"text":"Complete the table of values for $y = 2x + 3$","location":"specification"}]},{"type":"text","order":1,"title":"Use calculator table function","content":"Using a scientific calculator's table mode allows us to enter the function and generate all the values at once.","calculator":[{"gdc":{"expression":"2*x + 3","instructions":"1. Go to the Table menu.\n2. Enter the formula as \$Y = 2X + 3\$.\n3. Set the table range: Start = -2, End = 3, Step = 1.\n4. Display the table to read the corresponding Y-values for each X."},"ti84":{"expression":"2*X + 3","instructions":"1. Press [mode] and select 'TABLE' (or press [Y=] on a graphing calculator).\n2. Input the equation as \$Y_1 = 2X + 3\$.\n3. Press [2nd] [window] (TblSet) and set TblStart = -2 and \$\\Delta\\text{Tbl} = 1\$.\n4. Press [2nd] [graph] (Table) to view the table of values."},"desmos":{"expression":"y_1 = 2*x_1 + 3","instructions":"1. Click the '+' button and select 'Table'.\n2. In the column header, change \$y_1\$ to \$2x_1 + 3\$.\n3. In the \$x_1\$ column, type the values: -2, -1, 0, 1, 2, 3.\n4. The corresponding \$y_1\$ values will be automatically computed and shown."},"description":"Set up a table of values for $f(x) = 2x + 3$ starting at $-2$ and ending at $3$ with a step of $1$."}]},{"type":"text","order":2,"title":"Record the table values","content":"From the calculator's generated table, we find the following pairs:\n\n* When $x = -2$, $y = -1$\n* When $x = -1$, $y = 1$\n* When $x = 0$, $y = 3$\n* When $x = 1$, $y = 5$\n* When $x = 2$, $y = 7$\n* When $x = 3$, $y = 9$"},{"type":"text","order":3,"title":"Complete the table","content":"Now we can write the completed table of values:\n\n| $x$ | -2 | -1 | 0 | 1 | 2 | 3 |\n| :--- | :--- | :--- | :--- | :--- | :--- | :--- |\n| $y$ | **-1** | **1** | **3** | **5** | **7** | **9** |\n\n*Note on marking:* You earn 2 marks for having all values correct, and 1 mark if you get 2 or 3 of the values correct."}]},{"id":"bffe73cc-0227-4638-be2b-2605368696dd:table_of_values","label":"(b) Table of Values","steps":[{"type":"text","order":0,"title":"Set up a table","content":"To draw the graph of the equation $$y = 2x + 3$$ for $x$-values from $-2$ to $3$, we will construct a table of values. This will give us the coordinate pairs $(x, y)$ that we need to plot on the grid.\n\nLet's choose the integer values of $x$ in this range:\n\n$$\\begin{array}{|c|c|c|c|c|c|c|} \n\\hline \nx & -2 & -1 & 0 & 1 & 2 & 3 \\\\ \n\\hline \ny & & & & & & \\\\ \n\\hline \n\\end{array}$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$y = 2\\htmlData{anchor=x-var}{\\color{@sky}{x}} + 3$"},{"latex":"$$\\begin{aligned} \\text{For } \\htmlData{anchor=x-neg2}{\\color{@sky}{x = -2}} & \\implies y = 2(\\color{@sky}{-2}) + 3 = \\htmlData{anchor=y-neg1}{\\color{@amber}{-1}} \\\\ \\text{For } \\htmlData{anchor=x-neg1}{\\color{@sky}{x = -1}} & \\implies y = 2(\\color{@sky}{-1}) + 3 = \\htmlData{anchor=y-1}{\\color{@amber}{1}} \\\\ \\text{For } \\htmlData{anchor=x-0}{\\color{@sky}{x = 0}} & \\implies y = 2(\\color{@sky}{0}) + 3 = \\htmlData{anchor=y-3}{\\color{@amber}{3}} \\\\ \\text{For } \\htmlData{anchor=x-1}{\\color{@sky}{x = 1}} & \\implies y = 2(\\color{@sky}{1}) + 3 = \\htmlData{anchor=y-5}{\\color{@amber}{5}} \\\\ \\text{For } \\htmlData{anchor=x-2}{\\color{@sky}{x = 2}} & \\implies y = 2(\\color{@sky}{2}) + 3 = \\htmlData{anchor=y-7}{\\color{@amber}{7}} \\\\ \\text{For } \\htmlData{anchor=x-3}{\\color{@sky}{x = 3}} & \\implies y = 2(\\color{@sky}{3}) + 3 = \\htmlData{anchor=y-9}{\\color{@amber}{9}} \\end{aligned}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"x-neg2"},{"color":"amber","style":"text-color","anchor":"y-neg1"}],"connections":[{"to":"x-neg2","from":"x-var","color":"sky","label":null,"style":"solid"}]},"order":1,"title":"Calculate the y-coordinates","description":"Substitute each $x$-value into the equation $y = 2x + 3$ to compute the corresponding $y$-value."},{"type":"text","order":2,"title":"Complete the table","content":"Now we fill in the calculated $y$-values into our table:\n\n$$\\begin{array}{|c|c|c|c|c|c|c|} \n\\hline \nx & -2 & -1 & 0 & 1 & 2 & 3 \\\\ \n\\hline \ny & -1 & 1 & 3 & 5 & 7 & 9 \\\\ \n\\hline \n\\end{array}$$\n\nThis gives us six coordinate points to plot:\n$$(-2, -1), \\; (-1, 1), \\; (0, 3), \\; (1, 5), \\; (2, 7), \\; (3, 9)$$"},{"type":"text","order":3,"title":"Plot the points","content":"Plot each of these coordinates carefully on the grid:\n\n* Go left $2$ units and down $1$ unit to plot $(-2, -1)$\n* Go left $1$ unit and up $1$ unit to plot $(-1, 1)$\n* Mark the $y$-intercept at $(0, 3)$\n* Go right $1$ unit and up $5$ units to plot $(1, 5)$\n* Go right $2$ units and up $7$ units to plot $(2, 7)$\n* Go right $3$ units and up $9$ units to plot $(3, 9)$\n\n*Successfully plotting these coordinates correctly on your grid earns you the first method mark (\\textbf{M1}).*"},{"type":"text","order":4,"title":"Draw the straight line","content":"Use a ruler to draw a straight line passing through all your plotted points.\n\nMake sure your line starts exactly at $x = -2$ and extends to $x = 3$ to cover the full requested range.\n\n*Drawing the correct straight line through these points from $x = -2$ to $x = 3$ earns you the final accuracy mark (\\textbf{A1}).*"}]},{"id":"bffe73cc-0227-4638-be2b-2605368696dd:gradient_intercept","label":"(b) Gradient-Intercept Method","steps":[{"type":"text","order":0,"title":"Identify the key components","content":"To graph the line using the gradient-intercept method, we compare our equation to the standard form of a linear equation:\n\n$$y = mx + c$$\n\nWhere:\n- $m$ is the **gradient** (slope)\n- $c$ is the **y-intercept** (where the line crosses the y-axis)\n\nFor our equation $y = 2x + 3$, we have:\n- Gradient ($m$) = $2$\n- y-intercept ($c$) = $3$","highlights":[{"text":"y = 2x + 3","location":"specification"}]},{"type":"text","order":1,"title":"Plot the y-intercept","content":"The y-intercept is at the point where $x = 0$.\n\nSince our y-intercept is $3$, the first point we plot on the grid is:\n\n$$(0, 3)$$\n\nFind $3$ on the vertical y-axis and place a cross there."},{"type":"text","order":2,"title":"Use gradient for more points","content":"The gradient is $2$, which can be thought of as a fraction: $\\frac{2}{1}$.\n\n$$\\text{Gradient} = \\frac{\\text{Change in } y}{\\text{Change in } x} = \\frac{2}{1}$$\n\nThis means for every $1$ unit we move to the right (positive x-direction), we go **up by $2$ units** (positive y-direction):\n- From $(0, 3)$, go right $1$ and up $2$ to plot $(1, 5)$.\n- From $(1, 5)$, go right $1$ and up $2$ to plot $(2, 7)$.\n- From $(2, 7)$, go right $1$ and up $2$ to plot $(3, 9)$.\n\nWe can also go backwards by moving left $1$ and **down $2$**:\n- From $(0, 3)$, go left $1$ and down $2$ to plot $(-1, 1)$.\n- From $(-1, 1)$, go left $1$ and down $2$ to plot $(-2, -1)$."},{"type":"text","order":3,"title":"Draw the line","content":"Using a ruler, draw a single, straight line passing through all your plotted points.\n\nMake sure your line extends fully from $x = -2$ to $x = 3$ to cover the entire range requested in the question.\n\n- The leftmost point on your line should be at $(-2, -1)$.\n- The rightmost point on your line should be at $(3, 9)$.","highlights":[{"text":"for values of x from -2 to 3","location":"specification"}]}]}],"generatedAt":"2026-06-13T04:57:20.149Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"b65edc97-d6a4-4cc6-886f-d5b0dc306038","revisionId":"3993337a-ec98-43a9-9688-923b89427863","questionNumber":null,"questionType":"LA","specification":"","difficultyBand":"easy","tier":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":false,"parts":[{"id":"27277ab7-dfb3-4712-bf86-90615422ff54","label":"a","content":"On the grid, draw the graph of $y = 5 - 2x$ for values of $x$ from -1 to 4\n\n![A coordinate grid for drawing the graph of y = 5 - 2x.](https://assets.mathsgenie.co.uk/figures/coords/69d10acc092d4ccea5a6d5dac40ee3e4ae86afd02f7cdae5cb7ffff299274b9f.png)","markscheme":"- Correct table of values or at least 2 points correctly calculated B1\n- Points plotted correctly M1\n- Correct straight line drawn from $x = -1$ to $x = 4$ A1\n\n![Solution](https://assets.mathsgenie.co.uk/figures/coords/d4f41cef1906abb673f282d5eec5f63761e0955f0cf9ba17b794b4e3b5381162.png)","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct table of values or at least 2 points correctly calculated (e.g., (-1, 7), (0, 5), (4, -3))","code":"B"},{"id":"p2","marks":1,"description":"At least 2 points plotted correctly from their table or calculations","code":"M"},{"id":"p3","marks":1,"description":"A fully correct straight line drawn from x = -1 to x = 4","code":"A"}],"finalAnswers":["y = 5 - 2x"],"generatedAt":"2026-05-06T14:00:09.316Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"table-values","label":"Table of values","steps":[{"type":"text","order":0,"title":"Make a value table","content":"Use whole-number $x$-values from $-1$ to $4$. Substitute each into $y=5-2x$.\n\n| $x$ | $y$ |\n|---:|---:|\n| $-1$ | **$7$** |\n| $0$ | **$5$** |\n| $1$ | **$3$** |\n| $2$ | **$1$** |\n| $3$ | **$-1$** |\n| $4$ | **$-3$** |\n\nThis correct table earns the **B1** mark. Even though two correct points are enough for that mark, using several makes plotting the straight line much safer.","highlights":[{"text":"for values of $x$ from -1 to 4","location":"specification"}]},{"type":"text","order":1,"title":"Plot each coordinate","content":"Each row becomes a coordinate $(x,y)$: move across to the $x$-value first, then up or down to the $y$-value. Plot\n\n$$(-1,7),\\ (0,5),\\ (1,3),\\ (2,1),\\ (3,-1),\\ (4,-3).$$\n\nAccurate plotting earns the **M1** mark. A common slip is to reverse a coordinate: for example, $(1,3)$ means $1$ across and $3$ up, not the other way round."},{"type":"text","order":2,"title":"Draw the line","content":"Use a ruler to join the plotted points with one straight line. Stop the line at the points where $x=-1$ and $x=4$; do not extend it beyond those values.\n\nThat correctly drawn line earns the **A1** mark, completing the graph of\n\n$$\\boxed{y=5-2x\\text{ for }-1\\le x\\le4}.$$","highlights":[{"text":"draw the graph of $y = 5 - 2x$","location":"specification"}]}]},{"id":"intercept-gradient","label":"Intercept and gradient","steps":[{"type":"text","order":0,"title":"Find the starting point","content":"The equation is in the form $y=5-2x$. When $x=0$, the $-2x$ term is zero, so the line crosses the $y$-axis at $(0,5)$. Plot this point first: it is the **$y$-intercept**.\n\nThis is one correctly calculated point towards the first mark.","highlights":[{"text":"$$y = 5 - 2x$","location":"specification"}]},{"type":"drawing","order":1,"title":"Follow the gradient","width":512,"height":709,"shapes":[{"id":"grid-gx-2","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":654.1},{"x":100.3,"y":85.5}]},{"id":"grid-gx-1","dash":"dotted","type":"line","color":"grey","points":[{"x":147.7,"y":654.1},{"x":147.7,"y":85.5}]},{"id":"grid-gx0","dash":"dotted","type":"line","color":"grey","points":[{"x":195,"y":654.1},{"x":195,"y":85.5}]},{"id":"grid-gx1","dash":"dotted","type":"line","color":"grey","points":[{"x":242.4,"y":654.1},{"x":242.4,"y":85.5}]},{"id":"grid-gx2","dash":"dotted","type":"line","color":"grey","points":[{"x":289.8,"y":654.1},{"x":289.8,"y":85.5}]},{"id":"grid-gx3","dash":"dotted","type":"line","color":"grey","points":[{"x":337.2,"y":654.1},{"x":337.2,"y":85.5}]},{"id":"grid-gx4","dash":"dotted","type":"line","color":"grey","points":[{"x":384.6,"y":654.1},{"x":384.6,"y":85.5}]},{"id":"grid-gx5","dash":"dotted","type":"line","color":"grey","points":[{"x":432,"y":654.1},{"x":432,"y":85.5}]},{"id":"grid-gy-4","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":654.1},{"x":432,"y":654.1}]},{"id":"grid-gy-3","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":606.7},{"x":432,"y":606.7}]},{"id":"grid-gy-2","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":559.3},{"x":432,"y":559.3}]},{"id":"grid-gy-1","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":511.9},{"x":432,"y":511.9}]},{"id":"grid-gy0","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":464.5},{"x":432,"y":464.5}]},{"id":"grid-gy1","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":417.1},{"x":432,"y":417.1}]},{"id":"grid-gy2","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":369.8},{"x":432,"y":369.8}]},{"id":"grid-gy3","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":322.4},{"x":432,"y":322.4}]},{"id":"grid-gy4","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":275},{"x":432,"y":275}]},{"id":"grid-gy5","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":227.6},{"x":432,"y":227.6}]},{"id":"grid-gy6","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":180.2},{"x":432,"y":180.2}]},{"id":"grid-gy7","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":132.8},{"x":432,"y":132.8}]},{"id":"grid-gy8","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":85.5},{"x":432,"y":85.5}]},{"id":"grid-xaxis","toX":450.9,"toY":464.5,"type":"arrow","color":"black","fromX":90.8,"fromY":464.5},{"id":"grid-yaxis","toX":195,"toY":66.5,"type":"arrow","color":"black","fromX":195,"fromY":663.5},{"id":"seg-P0P1","toX":242.4,"toY":322.4,"type":"arrow","color":"blue","fromX":195,"fromY":227.6},{"id":"seg-P0Pm","toX":147.7,"toY":132.8,"type":"arrow","color":"blue","fromX":195,"fromY":227.6},{"h":8,"w":8,"x":191,"y":223.6,"id":"pt-P0","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":238.4,"y":318.4,"id":"pt-P1","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":285.8,"y":413.1,"id":"pt-P2","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":333.2,"y":507.9,"id":"pt-P3","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":380.6,"y":602.7,"id":"pt-P4","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":143.7,"y":128.8,"id":"pt-Pm","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"x":88.7,"y":468,"id":"grid-tx-2","size":"s","text":"-2","type":"text"},{"x":138.7,"y":468,"id":"grid-tx-1","size":"s","text":"-1","type":"text"},{"x":238.3,"y":468,"id":"grid-tx1","size":"s","text":"1","type":"text"},{"x":283,"y":468,"id":"grid-tx2","size":"s","text":"2","type":"text"},{"x":330.4,"y":468,"id":"grid-tx3","size":"s","text":"3","type":"text"},{"x":377.8,"y":468,"id":"grid-tx4","size":"s","text":"4","type":"text"},{"x":426,"y":468,"id":"grid-tx5","size":"s","text":"5","type":"text"},{"x":167.5,"y":641.6,"id":"grid-ty-4","size":"s","text":"-4","type":"text"},{"x":167.5,"y":594.2,"id":"grid-ty-3","size":"s","text":"-3","type":"text"},{"x":167.5,"y":546.8,"id":"grid-ty-2","size":"s","text":"-2","type":"text"},{"x":170.1,"y":499.4,"id":"grid-ty-1","size":"s","text":"-1","type":"text"},{"x":174.9,"y":404.6,"id":"grid-ty1","size":"s","text":"1","type":"text"},{"x":172.3,"y":357.3,"id":"grid-ty2","size":"s","text":"2","type":"text"},{"x":172.3,"y":309.9,"id":"grid-ty3","size":"s","text":"3","type":"text"},{"x":172.3,"y":262.5,"id":"grid-ty4","size":"s","text":"4","type":"text"},{"x":173.1,"y":215.1,"id":"grid-ty5","size":"s","text":"5","type":"text"},{"x":172.3,"y":167.7,"id":"grid-ty6","size":"s","text":"6","type":"text"},{"x":172.3,"y":120.3,"id":"grid-ty7","size":"s","text":"7","type":"text"},{"x":172.3,"y":73,"id":"grid-ty8","size":"s","text":"8","type":"text"},{"x":459.7,"y":440,"id":"grid-xlabel","size":"s","text":"x","type":"text"},{"x":201.4,"y":42,"id":"grid-ylabel","size":"s","text":"y","type":"text"},{"x":211.7,"y":190.1,"id":"pt-P0-label","text":" ","type":"text","color":"blue"},{"x":259.1,"y":284.8,"id":"pt-P1-label","text":" ","type":"text","color":"blue"},{"x":306.5,"y":379.6,"id":"pt-P2-label","text":" ","type":"text","color":"blue"},{"x":353.9,"y":474.4,"id":"pt-P3-label","text":" ","type":"text","color":"blue"},{"x":296.2,"y":632.2,"id":"pt-P4-label","text":"(4, −3)","type":"text","color":"blue"},{"x":64.5,"y":76,"id":"pt-Pm-label","text":"(−1, 7)","type":"text","color":"blue"},{"x":226.6,"y":184.3,"id":"label-1","size":"s","text":"(0, 5)","type":"text","color":"blue"},{"x":238.2,"y":243.5,"id":"label-2","size":"s","text":"1 right, 2 down","type":"text","color":"blue"},{"x":42,"y":203.3,"id":"label-3","size":"s","text":"1 left, 2 up","type":"text","color":"blue"}],"caption":"The gradient is −2: move 1 square right and 2 squares down from the intercept. Repeating this gives all the plotted points; reverse the move once to reach the point at x = −1.","diagramSpec":{"grid":{"xMax":5,"xMin":-2,"yMax":8,"yMin":-4,"showAxes":true,"showGrid":true},"points":[{"at":[0,5],"name":"P0"},{"at":[1,3],"name":"P1"},{"at":[2,1],"name":"P2"},{"at":[3,-1],"name":"P3"},{"at":[4,-3],"name":"P4"},{"at":[-1,7],"name":"Pm"}],"elements":[{"to":"P1","from":"P0","kind":"segment","color":"blue","arrows":"end"},{"to":"Pm","from":"P0","kind":"segment","color":"blue","arrows":"end"},{"at":"P0","kind":"point","color":"blue","label":" "},{"at":"P1","kind":"point","color":"blue","label":" "},{"at":"P2","kind":"point","color":"blue","label":" "},{"at":"P3","kind":"point","color":"blue","label":" "},{"at":"P4","kind":"point","color":"blue","label":"(4, −3)","labelDir":"below-left"},{"at":"Pm","kind":"point","color":"blue","label":"(−1, 7)","labelDir":"above-left"},{"at":[0.65,5.65],"kind":"label","size":"s","text":"(0, 5)","color":"blue"},{"at":[1.9,4.4],"kind":"label","size":"s","text":"1 right, 2 down","color":"blue"},{"at":[-1.55,5.25],"kind":"label","size":"s","text":"1 left, 2 up","color":"blue"}]}},{"type":"text","order":2,"title":"Plot the remaining points","content":"From $(0,5)$, repeat **1 right, 2 down** to plot $(1,3)$, $(2,1)$, $(3,-1)$ and $(4,-3)$. To get the point to the left, reverse the move: **1 left, 2 up** gives $(-1,7)$.\n\nPlotting these accurately earns the **M1** mark. Notice that a negative gradient makes the line slope downwards from left to right."},{"type":"text","order":3,"title":"Draw only the segment","content":"Use a ruler to draw one straight line through the plotted points. It must start at $x=-1$ and stop at $x=4$, so its endpoints are $(-1,7)$ and $(4,-3)$.\n\nDo not extend the line beyond these values of $x$. This correct straight-line segment earns the **A1** mark.","highlights":[{"text":"for values of $x$ from -1 to 4","location":"specification"}]}]}],"generatedAt":"2026-09-01T09:17:03.636Z","modelVersion":"gpt-5.6-terra+diagrams-2","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"27277ab7-dfb3-4712-bf86-90615422ff54:table-values","label":"Table of values","steps":[{"type":"text","order":0,"title":"Make a value table","content":"Use whole-number $x$-values from $-1$ to $4$. Substitute each into $y=5-2x$.\n\n| $x$ | $y$ |\n|---:|---:|\n| $-1$ | **$7$** |\n| $0$ | **$5$** |\n| $1$ | **$3$** |\n| $2$ | **$1$** |\n| $3$ | **$-1$** |\n| $4$ | **$-3$** |\n\nThis correct table earns the **B1** mark. Even though two correct points are enough for that mark, using several makes plotting the straight line much safer.","highlights":[{"text":"for values of $x$ from -1 to 4","location":"specification"}]},{"type":"text","order":1,"title":"Plot each coordinate","content":"Each row becomes a coordinate $(x,y)$: move across to the $x$-value first, then up or down to the $y$-value. Plot\n\n$$(-1,7),\\ (0,5),\\ (1,3),\\ (2,1),\\ (3,-1),\\ (4,-3).$$\n\nAccurate plotting earns the **M1** mark. A common slip is to reverse a coordinate: for example, $(1,3)$ means $1$ across and $3$ up, not the other way round."},{"type":"text","order":2,"title":"Draw the line","content":"Use a ruler to join the plotted points with one straight line. Stop the line at the points where $x=-1$ and $x=4$; do not extend it beyond those values.\n\nThat correctly drawn line earns the **A1** mark, completing the graph of\n\n$$\\boxed{y=5-2x\\text{ for }-1\\le x\\le4}.$$","highlights":[{"text":"draw the graph of $y = 5 - 2x$","location":"specification"}]}]},{"id":"27277ab7-dfb3-4712-bf86-90615422ff54:intercept-gradient","label":"Intercept and gradient","steps":[{"type":"text","order":0,"title":"Find the starting point","content":"The equation is in the form $y=5-2x$. When $x=0$, the $-2x$ term is zero, so the line crosses the $y$-axis at $(0,5)$. Plot this point first: it is the **$y$-intercept**.\n\nThis is one correctly calculated point towards the first mark.","highlights":[{"text":"$$y = 5 - 2x$","location":"specification"}]},{"type":"drawing","order":1,"title":"Follow the gradient","width":512,"height":709,"shapes":[{"id":"grid-gx-2","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":654.1},{"x":100.3,"y":85.5}]},{"id":"grid-gx-1","dash":"dotted","type":"line","color":"grey","points":[{"x":147.7,"y":654.1},{"x":147.7,"y":85.5}]},{"id":"grid-gx0","dash":"dotted","type":"line","color":"grey","points":[{"x":195,"y":654.1},{"x":195,"y":85.5}]},{"id":"grid-gx1","dash":"dotted","type":"line","color":"grey","points":[{"x":242.4,"y":654.1},{"x":242.4,"y":85.5}]},{"id":"grid-gx2","dash":"dotted","type":"line","color":"grey","points":[{"x":289.8,"y":654.1},{"x":289.8,"y":85.5}]},{"id":"grid-gx3","dash":"dotted","type":"line","color":"grey","points":[{"x":337.2,"y":654.1},{"x":337.2,"y":85.5}]},{"id":"grid-gx4","dash":"dotted","type":"line","color":"grey","points":[{"x":384.6,"y":654.1},{"x":384.6,"y":85.5}]},{"id":"grid-gx5","dash":"dotted","type":"line","color":"grey","points":[{"x":432,"y":654.1},{"x":432,"y":85.5}]},{"id":"grid-gy-4","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":654.1},{"x":432,"y":654.1}]},{"id":"grid-gy-3","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":606.7},{"x":432,"y":606.7}]},{"id":"grid-gy-2","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":559.3},{"x":432,"y":559.3}]},{"id":"grid-gy-1","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":511.9},{"x":432,"y":511.9}]},{"id":"grid-gy0","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":464.5},{"x":432,"y":464.5}]},{"id":"grid-gy1","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":417.1},{"x":432,"y":417.1}]},{"id":"grid-gy2","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":369.8},{"x":432,"y":369.8}]},{"id":"grid-gy3","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":322.4},{"x":432,"y":322.4}]},{"id":"grid-gy4","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":275},{"x":432,"y":275}]},{"id":"grid-gy5","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":227.6},{"x":432,"y":227.6}]},{"id":"grid-gy6","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":180.2},{"x":432,"y":180.2}]},{"id":"grid-gy7","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":132.8},{"x":432,"y":132.8}]},{"id":"grid-gy8","dash":"dotted","type":"line","color":"grey","points":[{"x":100.3,"y":85.5},{"x":432,"y":85.5}]},{"id":"grid-xaxis","toX":450.9,"toY":464.5,"type":"arrow","color":"black","fromX":90.8,"fromY":464.5},{"id":"grid-yaxis","toX":195,"toY":66.5,"type":"arrow","color":"black","fromX":195,"fromY":663.5},{"id":"seg-P0P1","toX":242.4,"toY":322.4,"type":"arrow","color":"blue","fromX":195,"fromY":227.6},{"id":"seg-P0Pm","toX":147.7,"toY":132.8,"type":"arrow","color":"blue","fromX":195,"fromY":227.6},{"h":8,"w":8,"x":191,"y":223.6,"id":"pt-P0","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":238.4,"y":318.4,"id":"pt-P1","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":285.8,"y":413.1,"id":"pt-P2","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":333.2,"y":507.9,"id":"pt-P3","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":380.6,"y":602.7,"id":"pt-P4","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"h":8,"w":8,"x":143.7,"y":128.8,"id":"pt-Pm","geo":"ellipse","fill":"solid","type":"geo","color":"blue"},{"x":88.7,"y":468,"id":"grid-tx-2","size":"s","text":"-2","type":"text"},{"x":138.7,"y":468,"id":"grid-tx-1","size":"s","text":"-1","type":"text"},{"x":238.3,"y":468,"id":"grid-tx1","size":"s","text":"1","type":"text"},{"x":283,"y":468,"id":"grid-tx2","size":"s","text":"2","type":"text"},{"x":330.4,"y":468,"id":"grid-tx3","size":"s","text":"3","type":"text"},{"x":377.8,"y":468,"id":"grid-tx4","size":"s","text":"4","type":"text"},{"x":426,"y":468,"id":"grid-tx5","size":"s","text":"5","type":"text"},{"x":167.5,"y":641.6,"id":"grid-ty-4","size":"s","text":"-4","type":"text"},{"x":167.5,"y":594.2,"id":"grid-ty-3","size":"s","text":"-3","type":"text"},{"x":167.5,"y":546.8,"id":"grid-ty-2","size":"s","text":"-2","type":"text"},{"x":170.1,"y":499.4,"id":"grid-ty-1","size":"s","text":"-1","type":"text"},{"x":174.9,"y":404.6,"id":"grid-ty1","size":"s","text":"1","type":"text"},{"x":172.3,"y":357.3,"id":"grid-ty2","size":"s","text":"2","type":"text"},{"x":172.3,"y":309.9,"id":"grid-ty3","size":"s","text":"3","type":"text"},{"x":172.3,"y":262.5,"id":"grid-ty4","size":"s","text":"4","type":"text"},{"x":173.1,"y":215.1,"id":"grid-ty5","size":"s","text":"5","type":"text"},{"x":172.3,"y":167.7,"id":"grid-ty6","size":"s","text":"6","type":"text"},{"x":172.3,"y":120.3,"id":"grid-ty7","size":"s","text":"7","type":"text"},{"x":172.3,"y":73,"id":"grid-ty8","size":"s","text":"8","type":"text"},{"x":459.7,"y":440,"id":"grid-xlabel","size":"s","text":"x","type":"text"},{"x":201.4,"y":42,"id":"grid-ylabel","size":"s","text":"y","type":"text"},{"x":211.7,"y":190.1,"id":"pt-P0-label","text":" ","type":"text","color":"blue"},{"x":259.1,"y":284.8,"id":"pt-P1-label","text":" ","type":"text","color":"blue"},{"x":306.5,"y":379.6,"id":"pt-P2-label","text":" ","type":"text","color":"blue"},{"x":353.9,"y":474.4,"id":"pt-P3-label","text":" ","type":"text","color":"blue"},{"x":296.2,"y":632.2,"id":"pt-P4-label","text":"(4, −3)","type":"text","color":"blue"},{"x":64.5,"y":76,"id":"pt-Pm-label","text":"(−1, 7)","type":"text","color":"blue"},{"x":226.6,"y":184.3,"id":"label-1","size":"s","text":"(0, 5)","type":"text","color":"blue"},{"x":238.2,"y":243.5,"id":"label-2","size":"s","text":"1 right, 2 down","type":"text","color":"blue"},{"x":42,"y":203.3,"id":"label-3","size":"s","text":"1 left, 2 up","type":"text","color":"blue"}],"caption":"The gradient is −2: move 1 square right and 2 squares down from the intercept. Repeating this gives all the plotted points; reverse the move once to reach the point at x = −1.","diagramSpec":{"grid":{"xMax":5,"xMin":-2,"yMax":8,"yMin":-4,"showAxes":true,"showGrid":true},"points":[{"at":[0,5],"name":"P0"},{"at":[1,3],"name":"P1"},{"at":[2,1],"name":"P2"},{"at":[3,-1],"name":"P3"},{"at":[4,-3],"name":"P4"},{"at":[-1,7],"name":"Pm"}],"elements":[{"to":"P1","from":"P0","kind":"segment","color":"blue","arrows":"end"},{"to":"Pm","from":"P0","kind":"segment","color":"blue","arrows":"end"},{"at":"P0","kind":"point","color":"blue","label":" "},{"at":"P1","kind":"point","color":"blue","label":" "},{"at":"P2","kind":"point","color":"blue","label":" "},{"at":"P3","kind":"point","color":"blue","label":" "},{"at":"P4","kind":"point","color":"blue","label":"(4, −3)","labelDir":"below-left"},{"at":"Pm","kind":"point","color":"blue","label":"(−1, 7)","labelDir":"above-left"},{"at":[0.65,5.65],"kind":"label","size":"s","text":"(0, 5)","color":"blue"},{"at":[1.9,4.4],"kind":"label","size":"s","text":"1 right, 2 down","color":"blue"},{"at":[-1.55,5.25],"kind":"label","size":"s","text":"1 left, 2 up","color":"blue"}]}},{"type":"text","order":2,"title":"Plot the remaining points","content":"From $(0,5)$, repeat **1 right, 2 down** to plot $(1,3)$, $(2,1)$, $(3,-1)$ and $(4,-3)$. To get the point to the left, reverse the move: **1 left, 2 up** gives $(-1,7)$.\n\nPlotting these accurately earns the **M1** mark. Notice that a negative gradient makes the line slope downwards from left to right."},{"type":"text","order":3,"title":"Draw only the segment","content":"Use a ruler to draw one straight line through the plotted points. It must start at $x=-1$ and stop at $x=4$, so its endpoints are $(-1,7)$ and $(4,-3)$.\n\nDo not extend the line beyond these values of $x$. This correct straight-line segment earns the **A1** mark.","highlights":[{"text":"for values of $x$ from -1 to 4","location":"specification"}]}]}],"generatedAt":"2026-09-01T09:17:31.786Z","modelVersion":"gpt-5.6-sol+diagrams-2","explanationVersion":"v3"},"firstAttemptFullMarks":null,"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/review/67eca03d-4ac4-4832-99ef-f89d8acf9f60.mp4","durationSeconds":70,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/review/67eca03d-4ac4-4832-99ef-f89d8acf9f60.jpg"}},{"id":"cb6ae992-8d3f-4b40-b76b-0b90aa4af311","revisionId":"f4e2f7de-1b1f-4fa2-83ef-4d1aae171fee","questionNumber":null,"questionType":"LA","specification":"","difficultyBand":"easy","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":false,"parts":[{"id":"beb1e1ed-9a49-48fe-8cd5-60da7bff5260","label":"a","content":"Complete the table of values for $y = 3x + 1$\n\n| $x$ | -2 | -1 | 0 | 1 | 2 | 3 |\n|-----|----|----|---|---|---|---|\n| $y$ | | | | | | |","markscheme":"- Correct values in table: -5, -2, 1, 4, 7, 10 B2\n- Award 1 mark for 2 or 3 correct values B1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Award 1 mark for 2 or 3 correct values.","code":"B"},{"id":"p2","marks":1,"description":"Award 2nd mark for all 6 correct values (-5, -2, 1, 4, 7, 10).","code":"B"}],"finalAnswers":["-5, -2, 1, 4, 7, 10"],"generatedAt":"2026-05-06T14:00:10.089Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]},{"id":"512dcbcd-863e-46bf-a0ca-63b3bbb64f91","label":"b","content":"On the grid, draw the graph of $y = 3x + 1$ for values of $x$ from -2 to 3\n\n![A coordinate grid for drawing the graph of y = 3x + 1.](https://assets.mathsgenie.co.uk/figures/coords/427dc7bc7f690124ca631d8a4431d46cdde59fba141ead920dd34e5ee7a4165e.png)","markscheme":"- Points plotted correctly from table M1\n- Correct straight line drawn from $x = -2$ to $x = 3$ A1\n\n![Solution](https://assets.mathsgenie.co.uk/figures/coords/643ac6c7891250373f108204299081343ed42846a8a1cae407479b7f4ccb978b.png)","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Points from the table plotted correctly.","code":"M"},{"id":"p2","marks":1,"description":"A single straight line correctly drawn for the specified range.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-06T14:00:10.089Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"value_table","label":"Value table and straight line","steps":[{"type":"text","order":0,"title":"Choose the inputs","content":"Use the integer $x$-values across the required interval: $-2,-1,0,1,2,3$. For each one, substitute into $y=3x+1$ to find the point to plot.","highlights":[{"text":"for values of $x$ from -2 to 3","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$3(-2)+1=\\color{@sky}{\\htmlData{anchor=outneg2}{-5}}$"},{"latex":"$$3(-1)+1=\\color{@sky}{\\htmlData{anchor=outneg1}{-2}}$"},{"latex":"$$3(0)+1=\\color{@sky}{\\htmlData{anchor=out0}{1}}$"},{"latex":"$$3(1)+1=\\color{@sky}{\\htmlData{anchor=out1}{4}}$"},{"latex":"$$3(2)+1=\\color{@sky}{\\htmlData{anchor=out2}{7}}$"},{"latex":"$$3(3)+1=\\color{@sky}{\\htmlData{anchor=out3}{10}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"outneg2"},{"color":"sky","style":"text-color","anchor":"outneg1"},{"color":"sky","style":"text-color","anchor":"out0"},{"color":"sky","style":"text-color","anchor":"out1"}]},"order":1,"title":"Calculate the outputs","description":"For each input, multiply by three, then add one. These calculations give every point needed for the graph."},{"type":"graph","order":2,"title":"Plot the points","viewport":{"top":10.8,"left":-2.3,"right":3.4,"bottom":-6},"axisLabels":{"x":"x","y":"y"},"description":"Plot the six coordinates from the table: $(-2,-5)$, $(-1,-2)$, $(0,1)$, $(1,4)$, $(2,7)$ and $(3,10)$. Correctly plotted points earn M1.","expressions":[{"id":"expr-0","color":"sky","label":"(-2,-5)","latex":"(-2,-5)","pointStyle":"point","labelOrientation":"right"},{"id":"expr-1","color":"sky","label":"(-1,-2)","latex":"(-1,-2)","pointStyle":"point","labelOrientation":"right"},{"id":"expr-2","color":"sky","label":"(0,1)","latex":"(0,1)","pointStyle":"point","labelOrientation":"right"},{"id":"expr-3","color":"sky","label":"(1,4)","latex":"(1,4)","pointStyle":"point","labelOrientation":"right"},{"id":"expr-4","color":"sky","label":"(2,7)","latex":"(2,7)","pointStyle":"point","labelOrientation":"right"},{"id":"expr-5","color":"sky","label":"(3,10)","latex":"(3,10)","pointStyle":"point","labelOrientation":"left"}]},{"type":"graph","order":3,"title":"Join with a ruler","viewport":{"top":10.8,"left":-2.3,"right":3.4,"bottom":-6},"axisLabels":{"x":"x","y":"y"},"description":"Use a ruler to draw one straight line through the points, stopping at the required endpoints $(-2,-5)$ and $(3,10)$. The correct line over this full interval earns A1.","expressions":[{"id":"expr-0","color":"green","latex":"y=3x+1\\left\\{-2\\le x\\le3\\right\\}"},{"id":"expr-1","color":"green","label":"(-2,-5)","latex":"(-2,-5)","pointStyle":"point","labelOrientation":"right"},{"id":"expr-2","color":"sky","latex":"(-1,-2)","pointStyle":"point"},{"id":"expr-3","color":"sky","latex":"(0,1)","pointStyle":"point"},{"id":"expr-4","color":"sky","latex":"(1,4)","pointStyle":"point"},{"id":"expr-5","color":"sky","latex":"(2,7)","pointStyle":"point"},{"id":"expr-6","color":"green","label":"(3,10)","latex":"(3,10)","pointStyle":"point","labelOrientation":"left"},{"id":"expr-7","color":"green","label":"y=3x+1","latex":"(2.6,8.8)","hidden":true,"labelOrientation":"left"}]}]}],"generatedAt":"2026-07-19T07:43:16.750Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"gcse_maths__wjec","summaries":[{"id":"ed0aa6e6-7eca-4813-8fa3-4eaa899e51fc","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"146f04b9-0f2e-4a5d-b4e9-16ef2e6537eb","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"32f38b56-b569-426e-bb82-609aa610db6f","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"5b64a292-f3bc-4705-b27d-fa47ee4c895e","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"6b48c40a-1846-4e29-93af-909edd75d314","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"7d637825-43d1-4126-8b09-dbf53555d8ee","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"939a3eb8-84fb-41ae-b06b-f052759acde5","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"c398326d-d937-4500-b28f-744a330da057","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"eb97b467-0f4f-4010-a963-45b91c26515f","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"0134009f-49ea-441d-b56a-b46600816d62","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"2522da3c-350e-44e8-9e61-223627158528","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"84550a5b-91a4-4e7c-8614-8d1490af3583","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"b93bf801-786c-444f-8e31-fb543b9c7bd1","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"c2e9d857-8335-4e2d-9b9a-ec1305ec204c","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"ca2a3e1f-4ec6-4c43-888a-be2c9b581ce1","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"f7fb7b7c-a5f8-4efb-8c36-fcb76a0d51d8","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"d37511de-168d-44c3-8ed5-6cb203f91f77","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"13688535-664c-493a-92dc-826716346764","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"7229cab2-a3f5-4d31-bb6a-fa6b19e431be","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"9dc5f3ab-7d9a-4a10-9413-ec5d55184f36","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"b65edc97-d6a4-4cc6-886f-d5b0dc306038","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"c4f10484-831d-420c-b40a-cd4fb98d50ec","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"cb6ae992-8d3f-4b40-b76b-0b90aa4af311","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"cede7162-805d-46ce-b982-d9934f2bce05","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"2d296b62-9588-4e75-a464-ac80ddd20515","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"d2b96531-d36f-468e-8250-50c02df95fc1","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"d681bd52-e934-4b6d-9c08-9186a00e6570","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"ecaf5372-9646-4d22-bf8e-2ee8d685b027","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false}],"title":"Drawing Linear Graphs","topicId":"43b3ff0e-f970-fc63-7b68-b72092e4b3a4","topicSidebar":"$L3a","topicSlug":"grade-3-3-15-drawing-linear-graphs","topicTitle":"Drawing Linear Graphs"}]}],"$L3b","$L3c"]}]

Drawing Linear Graphs

Question 7

Drawing Linear Graphs Questions

Drawing Linear Graphs

Question 7

Drawing Linear Graphs Questions