81f-1e09-4aee-8232-e5a5141b0650","topicSlug":"straight-lines","cards":[{"id":"ff58f7a1-0b06-4cb0-87aa-fcf17caf802e","cardType":"cloze","front":"For points $(x_1,y_1)$ and $(x_2,y_2)$, the gradient is $\\text{[...]}$.","back":"For points $(x_1,y_1)$ and $(x_2,y_2)$, the gradient is $\\boxed{m=\\frac{y_2-y_1}{x_2-x_1}}$.","points":null,"mcqOptions":null},{"id":"d193975c-3eaf-449d-a464-c4613382db3d","cardType":"basic","front":"How does a line with positive gradient move as $x$ increases?","back":"It rises from left to right.","points":1,"mcqOptions":null},{"id":"eaaafb3d-38d1-4b6f-974d-c039c87170cf","cardType":"basic","front":"What does a larger gradient magnitude $|m|$ indicate?","back":"A steeper line.","points":1,"mcqOptions":null},{"id":"468e30d9-4ff9-4b89-bd92-4de14ee91f12","cardType":"basic","front":"What is the gradient of a horizontal line?","back":"The gradient is zero.","points":1,"mcqOptions":null},{"id":"23b27906-82d0-46d1-909c-97d52188f41f","cardType":"basic","front":"What form does the equation of a vertical line take?","back":"$x=k$, where $k$ is constant.","points":1,"mcqOptions":null},{"id":"e04d1d9c-b156-4703-8dba-2db0990f308b","cardType":"basic","front":"Why is the gradient of a vertical line undefined?","back":"Its $x$-coordinates are equal, so $x_2-x_1=0$.","points":2,"mcqOptions":null},{"id":"40e89a52-8697-4330-a7aa-c01bde56c7a2","cardType":"cloze","front":"In $y=mx+c$, $m$ is the [ ] and $c$ is the $y$-intercept.","back":"In $y=mx+c$, $m$ is the gradient and $c$ is the $y$-intercept.","points":null,"mcqOptions":null},{"id":"3a44e264-8415-4ed1-aa6e-abb957809a13","cardType":"cloze","front":"In $y=mx+c$, $m$ is the gradient and $c$ is the [ ].","back":"In $y=mx+c$, $m$ is the gradient and $c$ is the $y$-intercept.","points":null,"mcqOptions":null},{"id":"d10fb8ce-6b6e-4106-b6d0-c61a42fe9402","cardType":"basic","front":"Why does $y=mx+c$ cross the $y$-axis at $(0,c)$?","back":"On the $y$-axis, $x=0$, so $y=c$.","points":2,"mcqOptions":null},{"id":"d2b56449-c0ab-4eb8-84f0-b0d2c8f77359","cardType":"cloze","front":"A line with gradient $m$ through $(x_1,y_1)$ has equation $\\text{[...]}$.","back":"A line with gradient $m$ through $(x_1,y_1)$ has equation $\\boxed{y-y_1=m(x-x_1)}$.","points":null,"mcqOptions":null},{"id":"573b0d9c-8027-4944-b8da-0bfd979f3fa8","cardType":"basic","front":"Find the equation of the line with gradient $-\\frac{3}{2}$ and $y$-intercept $5$.","back":"$y=-\\frac{3}{2}x+5$","points":1,"mcqOptions":null},{"id":"b7de0f07-ca0d-4134-889c-c882747fb8c2","cardType":"basic","front":"When using the point $(-3,2)$, what does $x-x_1$ simplify to?","back":"$x+3$","points":1,"mcqOptions":null},{"id":"6bef1dca-23c4-4700-833e-09615da2b4a1","cardType":"basic","front":"Find the gradient through $(-2,5)$ and $(4,-7)$.","back":"$m=-2$","points":2,"mcqOptions":null},{"id":"2f70147f-3cac-477f-9bad-09a66addbacc","cardType":"basic","front":"What error occurs if only one coordinate difference is reversed in the gradient formula?","back":"The gradient has the incorrect sign.","points":1,"mcqOptions":null},{"id":"ca1c6eaf-e9c2-4f28-9149-0a8f261cb77e","cardType":"basic","front":"Find the equation of the line with gradient $4$ through $(-3,2)$.","back":"$y=4x+14$","points":2,"mcqOptions":null},{"id":"e49928e1-7599-41f7-8610-3643e2eae7fd","cardType":"basic","front":"Find the equation of the line through $(2,-1)$ and $(8,11)$.","back":"$y=2x-5$","points":3,"mcqOptions":null},{"id":"cf01294f-0f37-4526-942d-c17407e45df3","cardType":"cloze","front":"The general form is $\\text{[...]}$, where $a$ and $b$ are not both zero.","back":"The general form is $\\boxed{ax+by+c=0}$, where $a$ and $b$ are not bot

1.3.1 Straight lines Flashcards

1.3.1 Straight lines Flashcards