":"1.5.1 Equation of a straight line y = mx + c Flashcards","topicId":"edf51556-db45-4e24-9f7b-e65576d61d73","topicSlug":"equation-of-a-straight-line-y-mx-c","cards":[{"id":"5f260e72-c9d9-4fc2-aff8-6cb145ca68e0","cardType":"cloze","front":"In an ordered pair $(x,y)$, the first coordinate gives the [ ].","back":"In an ordered pair $(x,y)$, the first coordinate gives the horizontal position.","points":null,"mcqOptions":null},{"id":"ab1c0f29-2505-49f7-aec4-d8309c2e745c","cardType":"basic","front":"Does $(4,11)$ lie on $y=2x+3$?","back":"Yes, because $2(4)+3=11$.","points":1,"mcqOptions":null},{"id":"bf388304-015c-4282-b2dc-de7b87d2e37a","cardType":"cloze","front":"For two distinct points on a non-vertical line, the gradient is $\\text{[...]}$.","back":"For two distinct points on a non-vertical line, the gradient is $\\boxed{m=\\frac{y_2-y_1}{x_2-x_1}}$.","points":null,"mcqOptions":null},{"id":"ee7769c9-3214-4cdc-a8ea-f49a126ffb5f","cardType":"basic","front":"If a line has gradient $3$, how does $y$ change when $x$ increases by $1$?","back":"$$y$ increases by $3$.","points":1,"mcqOptions":null},{"id":"460a69da-574e-4990-a53f-5501709e085a","cardType":"basic","front":"If a line has gradient $-\\frac12$, how does $y$ change when $x$ increases by $2$?","back":"$$y$ decreases by $1$.","points":1,"mcqOptions":null},{"id":"5dcd8828-70d0-4951-8f7c-568f94011683","cardType":"cloze","front":"A line with $m>0$ [ ].","back":"A line with $m>0$ rises from left to right.","points":null,"mcqOptions":null},{"id":"8a92520f-e5a8-4e61-8993-688fbc0b1499","cardType":"basic","front":"Which is steeper: a line with gradient $-5$ or one with gradient $3$?","back":"The line with gradient $-5$, because $|-5|>|3|$.","points":2,"mcqOptions":null},{"id":"c2fc9208-417d-4f0d-b3db-edaea331302e","cardType":"basic","front":"Find the gradient through $(-2,5)$ and $(4,-7)$.","back":"$m=-2$.","points":2,"mcqOptions":null},{"id":"4315ade3-fd8f-4ed9-91ec-f2608df809b6","cardType":"basic","front":"What happens if the subtraction order is reversed in only one part of the gradient formula?","back":"The gradient has the wrong sign.","points":1,"mcqOptions":null},{"id":"1cda3ab4-f2cf-47a3-bc4d-392e381c6caa","cardType":"cloze","front":"In $y=mx+c$, the coefficient of $x$ is the [ ].","back":"In $y=mx+c$, the coefficient of $x$ is the gradient.","points":null,"mcqOptions":null},{"id":"b6e1e1c9-8357-4884-85d4-0560b19752d0","cardType":"cloze","front":"In $y=mx+c$, the line crosses the $y$-axis at $\\text{[...]}$.","back":"In $y=mx+c$, the line crosses the $y$-axis at $\\boxed{(0,c)}$.","points":null,"mcqOptions":null},{"id":"d9f8e4b1-c27b-4d75-82b9-f1a2f57d5d79","cardType":"basic","front":"For $y=-\\frac32x+6$, how does $y$ change when $x$ increases by $2$?","back":"$$y$ decreases by $3$.","points":1,"mcqOptions":null},{"id":"1ec884fe-b05a-46f1-bfef-24954495e52a","cardType":"basic","front":"Starting at the $y$-intercept of $y=\\frac23x-1$, which second integer-coordinate point can be found using the gradient?","back":"$(3,1)$.","points":2,"mcqOptions":null},{"id":"d16560cf-23e4-4af8-b8b4-fbbac03dd966","cardType":"basic","front":"A horizontal line passes through $(3,4)$. What is its equation?","back":"$y=4$.","points":1,"mcqOptions":null},{"id":"49a76b18-5d72-4659-a3a7-a96a23759c93","cardType":"basic","front":"A vertical line passes through $(-2,5)$. What is its equation?","back":"$x=-2$.","points":1,"mcqOptions":null},