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7)$","markscheme":"- Calculates gradient of A: $m = \\frac{10 - 1}{4 - (-2)} = \\frac{9}{6} = \\frac{3}{2}$ M1\n- Substitutes $(2, 7)$ into $y = \\frac{3}{2}x + c$: $7 = \\frac{3}{2}(2) + c \\implies c = 4$ M1\n- Final equation $y = \\frac{3}{2}x + 4$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the gradient of Line A as $\\frac{3}{2}$.","code":"M"},{"id":"p2","marks":1,"description":"Substitutes the point $(2, 7)$ into $y = \\frac{3}{2}x + c$ to find $c$.","code":"M"},{"id":"p3","marks":1,"description":"Correct final equation $y = \\frac{3}{2}x + 4$.","code":"A"}],"finalAnswers":["y=3/2x+4"],"generatedAt":"2026-05-07T02:03:01.197Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"gradient_then_intercept","label":"Gradient then intercept","steps":[{"type":"text","order":0,"title":"Use parallel gradients","content":"Parallel lines have the same gradient. So first find the gradient of line $A$ using its two given points.","highlights":[{"text":"Line A passes through the points $(-2, 1)$ and $(4, 10)$","location":"specification"},{"text":"parallel to A","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"m=\\frac{\\htmlData{anchor=rise}{\\color{@sky}{10-1}}}{\\htmlData{anchor=run}{\\color{@orange}{4-(-2)}}}"},{"latex":"m=\\frac{9}{6}"},{"latex":"m=\\frac{3}{2}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"rise"},{"color":"orange","style":"text-color","anchor":"run"}]},"order":1,"title":"Calculate the gradient","description":"Use the change in y divided by the change in x, keeping each subtraction in the same order. This calculation earns M1; parallel lines have the same gradient, so the required line has gradient three halves."},{"type":"hyper_latex","block":{"nodes":[{"latex":"y=\\frac{3}{2}x+c"},{"latex":"\\htmlData{anchor=seven}{\\color{@sky}{7}}=\\frac{3}{2}\\htmlData{anchor=two}{\\color{@sky}{(2)}}+c"},{"latex":"7=3+c"},{"latex":"\\htmlData{anchor=intercept}{c=4}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"two"}]},"order":3,"title":"Find the intercept","description":"Write the line as y = 3/2 x + c, then substitute the point it must pass through. This substitution earns the second mark (M1)."},{"type":"text","order":4,"title":"State the equation","content":"Substitute $c=4$ into the line equation:\n\n$$y=\\frac{3}{2}x+4$$\n\nThis is the required equation and earns the final accuracy mark (A1).","highlights":[{"text":"passes through $(2, 7)$","location":"specification"}]}]}],"generatedAt":"2026-07-21T04:05:24.479Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"4bb0fdaa-3145-4c69-b31a-7058b11ddbd8","revisionId":"76413c15-3d07-4108-b3cc-03dd310767dd","questionNumber":"15","questionType":"LA","specification":"Line A passes through the points $(2, -5)$ and $(10, -1)$ ","difficulty":3,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Parallel and Perpendicular Lines","calculatorUse":null,"isCalculation":true,"parts":[{"id":"ee9918fb-95e4-4285-80ee-a2697eb19f34","label":"0","content":"Find the equation of the line perpendicular to A that passes through $(4, 3)$","markscheme":"- Calculates gradient of A: $m = \\frac{-1 - (-5)}{10 - 2} = \\frac{4}{8} = \\frac{1}{2}$ M1\n- Perpendicular gradient $m = -2$ and substitutes $(4, 3)$: $3 = -2(4) + c \\implies c = 11$ M1\n- Final equation $y = -2x + 11$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Finds the perpendicular gradient $m = -2$.","code":"M"},{"id":"p2","marks":1,"description":"Correct final equation $y = -2x + 11$.","code":"A"}],"finalAnswers":["y=-2x+11"],"generatedAt":"2026-05-07T02:03:01.197Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":80},"walkthroughVideo":null}],"subjectCode":"igcse_maths__cie","summaries":[{"id":"acbe8ebb-46d9-478e-8f4d-932b2885f04c","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":true},{"id":"00df6036-9aab-4beb-a1f9-478482a7e43b","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"88754053-ce58-485c-a539-99de2a7000a2","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"99e9a58e-58ce-4c5b-bcf8-e1fc35241405","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":true},{"id":"5aa9fb76-4e85-46d4-9eb8-828c02ccc7a6","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"9b5feb40-0aa0-44e4-8ce6-453faebd020a","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"e0cb84a5-5545-4566-9b6a-7e816ee630e0","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"d258283c-865e-47c0-89da-0e5a1bcf9a81","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"91efa1cb-1437-4764-928f-184d64d102eb","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"6277a69d-6c9b-4e4d-a024-c4c43440a622","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"e3704fe4-d3b3-4d05-a5be-25f12b806bf9","difficultyBand":"medium","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"3e371dc2-7407-45d1-80db-f83b8384f7ae","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"279118c0-d7d5-42b6-8a6a-0acb5f408d8f","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c5bf0b85-9272-4d46-9a99-b4887b1793ec","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"4bb0fdaa-3145-4c69-b31a-7058b11ddbd8","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"a8a661f3-569f-4c77-a493-be9716343848","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c22eabf2-eada-4b44-bdb5-ceda01fdd864","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"f5aac4ae-4ceb-4ac8-9cdc-ca59354e843c","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"2db8e411-8c21-448e-ae58-f85a6e6f3962","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true}],"title":"Parallel and Perpendicular Lines","topicId":"697d56f9-6c2e-4572-b3fd-732756250220","topicSidebar":"$L3c","topicSlug":"grade-6-6-12-parallel-and-perpendicular-lines","topicTitle":"Parallel and Perpendicular Lines"}]}],"$L3d","$L3e"]}]

Parallel and Perpendicular Lines

Question 5

Parallel and Perpendicular Lines Questions

Parallel and Perpendicular Lines

Question 5

Parallel and Perpendicular Lines Questions