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

What is the equation of the line shown in the $xy$-plane below?

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","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-264"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

What is the equation of the line shown in the $xy$-plane below?

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

Choice B is correct. Any line in the $xy$-plane can be defined by an equation in the form $y=mx+b$, where $m$ is the slope of the line and $b$ is the y-coordinate of the y-intercept of the line. From the graph, the $y$-intercept of the line is $(0, 3)$. Therefore, $b=3$. The slope of the line is the change in the value of $y$ divided by the change in the value of $x$ for any two points on the line. The line shown passes through $(0, 3)$ and $(1, 0)$, so $m=\\dfrac{3-0}{0-1}$, or $m=-3$. Therefore, the equation of the line is $y=-3x+3$.

Choices A and C are incorrect because the equations given in these choices represent a line with a positive slope. However, the line shown has a negative slope. Choice D is incorrect because the equation given in this choice represents a line with a slope of $-\\dfrac{1}{3}$. However, the line shown has a slope of $-3$.

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

What is the equation of the line shown in the $xy$-plane below?

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

$y=3x-3$

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

$y=\\dfrac{1}{3}x-3$

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

$y=-\\dfrac{1}{3}x+3$

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

$y=-3x+3$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-264"}