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

What is the equation of the line that passes through the point $(0,5)$ and is parallel to the graph of $y=7x+4$ in the $xy$-plane?

","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-26"}],"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 that passes through the point $(0,5)$ and is parallel to the graph of $y=7x+4$ in the $xy$-plane?

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

Choice B is correct. The equation of a line in the $xy$-plane can be written in slope-intercept form $y=mx+b$, where $m$ is the slope of the line and $(0,b)$ is its $y$-intercept. It's given that the line passes through the point $(0,5)$. Therefore, $b=5$. It's also given that the line is parallel to the graph of $y=7x+4$, which means the line has the same slope as the graph of $y=7x+4$. The slope of the graph of $y=7x+4$ is $7$ Therefore, $m=7$ Substituting $7$ for $m$ and $5$ for $b$ in the equation $y=mx+b$ yields $y=7x+5$.

Choice A is incorrect. The graph of this equation passes through the point $(0,0)$, not $(0,5)$, and has a slope of 5, not 7.

Choice C is incorrect. The graph of this equation passes through the point $(0,0)$, not $(0,5)$

Choice D is incorrect. The graph of this equation passes through the point $(0,7)$, not $(0,5)$, and has a slope of 5, not 7.

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

What is the equation of the line that passes through the point $(0,5)$ and is parallel to the graph of $y=7x+4$ in the $xy$-plane?

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

$y=5x$

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

$y=7x$

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

$y=5x+7$

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

$y=7x+5$

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

Choice C is incorrect. The graph of this equation passes through the point $(0,0)$, not $(0,5)$

Choice D is incorrect. The graph of this equation passes through the point $(0,7)$, not $(0,5)$, and has a slope of 5, not 7.

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

Choice C is incorrect. The graph of this equation passes through the point $(0,0)$, not $(0,5)$

Choice D is incorrect. The graph of this equation passes through the point $(0,7)$, not $(0,5)$, and has a slope of 5, not 7.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-26"}