{"@context":"https://schema.org/","@type":"Quiz","name":"

In the $xy$-plane, line $k$ passes through the points $(0,-5)$ and $(1,-1)$. Which equation defines line $k$?

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In the $xy$-plane, line $k$ passes through the points $(0,-5)$ and $(1,-1)$. Which equation defines line $k$?

","comment":{"@type":"Comment","text":"

Choice D is correct. An equation defining a line in the $xy$-plane can be written in the form $y=mx+b$, where $m$ represents the slope and $(0,b)$ represents the $y$-intercept of the line. It's given that line $k$ passes through the point $(0,-5)$; therefore, $b=-5$. The slope, $m$, of a line can be found using any two points on the line, $(x_{1},y_{1})$ and $(x_{2},y_{2})$, and the slope formula $m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. Substituting the points $(0,-5)$ and $(1,-1)$ for $(x_{1},y_{1})$ and $(x_{2},y_{2})$, respectively, in the slope formula yields $m=\\frac{(-1-(-5))}{(1-0)}$, or $m=4$. Substituting $4$ for $m$ and $-5$ for $b$ in the equation $y=mx+b$ yields $y=4x-5$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

"},"encodingFormat":"text/markdown","text":"

In the $xy$-plane, line $k$ passes through the points $(0,-5)$ and $(1,-1)$. Which equation defines line $k$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$y=-x+\\frac{1}{4}$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$y=\\frac{1}{4}x-5$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

\$y=-x+4\$

"}],"acceptedAnswer":{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$y=4x-5$

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-150"}