l and perpendicular lines Flashcards","topicId":"b716c1d9-ac2f-4744-86be-caa765665be8","topicSlug":"parallel-and-perpendicular-lines","cards":[{"id":"63ec1215-6595-408c-b44b-b8f1a5ac286c","cardType":"basic","front":"How does a line with a positive gradient move from left to right?","back":"It rises.","points":1,"mcqOptions":null},{"id":"f92f7131-57cc-4b78-9084-74c440e0bbea","cardType":"basic","front":"How does a line with a negative gradient move from left to right?","back":"It falls.","points":1,"mcqOptions":null},{"id":"6cd83cc4-c47a-4fb4-9d1f-528dffb1b1ca","cardType":"basic","front":"What gradient does a horizontal line have?","back":"$0$","points":1,"mcqOptions":null},{"id":"25eef71d-851a-45a0-8689-cc7a17f25aa5","cardType":"basic","front":"Why is the gradient of a vertical line undefined?","back":"The gradient calculation requires division by zero.","points":2,"mcqOptions":null},{"id":"c81441af-59d4-417c-8061-2c7a6d80570f","cardType":"cloze","front":"The gradient through $(x_1,y_1)$ and $(x_2,y_2)$ is $\\text{[...]}$.","back":"The gradient through $(x_1,y_1)$ and $(x_2,y_2)$ is $\\boxed{m=\\frac{y_2-y_1}{x_2-x_1}}$.","points":null,"mcqOptions":null},{"id":"03f8f1c0-18b6-4f41-99e0-25150bbc823a","cardType":"basic","front":"What error occurs if the coordinate subtraction orders are inconsistent?","back":"The gradient has the wrong sign.","points":1,"mcqOptions":null},{"id":"f63daa2c-182d-4222-9f9c-069660fe685e","cardType":"cloze","front":"In $y=mx+c$, the gradient is $\\text{[...]}$.","back":"In $y=mx+c$, the gradient is $\\boxed{m}$.","points":null,"mcqOptions":null},{"id":"c2b7d5d3-c48e-4572-a5b4-d2fe822c252d","cardType":"basic","front":"What must you do before reading the gradient from a general line equation?","back":"Rearrange it into $y=mx+c$.","points":1,"mcqOptions":null},{"id":"f41fe093-fa89-4fce-9f4b-03a6dd678a8b","cardType":"basic","front":"Find the gradient of the line through $(-2,1)$ and $(4,10)$.","back":"$\\frac{3}{2}$","points":1,"mcqOptions":null},{"id":"0283788b-3227-42ce-bcd3-2ef7b24d8fda","cardType":"basic","front":"Find the gradient of $3x+2y=8$.","back":"$-\\frac{3}{2}$","points":1,"mcqOptions":null},{"id":"ad4c6eab-f137-463e-878f-e3715bfd7dd6","cardType":"cloze","front":"Non-vertical lines are parallel exactly when $\\text{[...]}$.","back":"Non-vertical lines are parallel exactly when $\\boxed{m_1=m_2}$.","points":null,"mcqOptions":null},{"id":"d4609eda-3d05-4c4b-8d95-10333d1d83c5","cardType":"basic","front":"How must the $y$-intercepts of distinct parallel non-vertical lines compare?","back":"They must be different.","points":1,"mcqOptions":null},{"id":"80487ae7-8cc2-4967-9dc9-1671a2238cd7","cardType":"basic","front":"What is the gradient perpendicular to $\\frac{3}{4}$?","back":"$-\\frac{4}{3}$","points":1,"mcqOptions":null},{"id":"67c28e05-b40b-479d-8996-61d80eda39af","cardType":"cloze","front":"For non-vertical perpendicular lines, $\\text{[...]}$.","back":"For non-vertical perpendicular lines, $\\boxed{m_1m_2=-1}$.","points":null,"mcqOptions":null},{"id":"b614bb79-8165-4c86-83f0-cf123a885248","cardType":"basic","front":"Why are gradients with opposite signs not necessarily perpendicular?","back":"Their product must be exactly $-1$.","points":2,"mcqOptions":null},{"id":"8b6b97a7-5f7d-4595-9404-ed954ca918bf","cardType":"cloze","front":"The point-gradient equation through $(x_1,y_1)$ is $\\text{[...]}$.","back":"The point-gradient equation through $(x_1,y_1)$ is $\\boxed{y-y_1=m(x-x_1)}$.","points":null,"mcqOptions":null},{"id":"248c24ca-d2d5-4a9e-94fc-289980dc847b","cardType":"basic","front":"Are $2x+5y=7$ and $5x-2y=3$ perpendicular? Justify using their gradients.","back":"Yes: $-\\frac25\\times\\frac52=-1$.","points":2,"mcqOptions":null},{"id":"2671f4a3-84d2-450b-84eb-7f4eccd99a8b","cardType":"basic","front":"Find the line parallel to $3x-2y=7$ through $(4,-1)$.","back":"$y=\\frac32x

1.3.2 Parallel and perpendicular lines Flashcards

1.3.2 Parallel and perpendicular lines Flashcards