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

Line $t$ in the $xy$-plane has a slope of $-\\frac{1}{3}$ and passes through the point $(9,10)$. Which equation defines line $t$?

","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-36"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

Line $t$ in the $xy$-plane has a slope of $-\\frac{1}{3}$ and passes through the point $(9,10)$. Which equation defines line $t$?

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

Choice D is correct. The equation that defines line $t$ in the $xy$-plane can be written in slope-intercept form $y=mx+b$, where $m$ is the slope of line $t$ and $(0,b)$ is its $y$-intercept. It's given that line $t$ has a slope of $-\\frac{1}{3}$. Therefore, $m=-\\frac{1}{3}$. Substituting $-\\frac{1}{3}$ for $m$ in the equation $y=mx+b$ yields $y=-\\frac{1}{3}x+b$, or $y=-\\frac{x}{3}+b$. It's also given that line $t$ passes through the point $(9,10)$. Substituting 9 for $x$ and 10 for $y$ in the equation $y=-\\frac{x}{3}+b$ yields $10=-\\frac{9}{3}+b$, or $10=-3+b$. Adding 3 to both sides of this equation yields $13=b$. Substituting 13 for $b$ in the equation $y=-\\frac{x}{3}+b$ yields $y=-\\frac{x}{3}+13$.

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

Choice B is incorrect. This equation defines a line that has a slope of 9, not $-\\frac{1}{3}$, and passes through the point $(0,10)$, not $(9,10)$.

Choice C is incorrect. This equation defines a line that passes through the point $(0,10)$, not $(9,10)$.

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

Line $t$ in the $xy$-plane has a slope of $-\\frac{1}{3}$ and passes through the point $(9,10)$. Which equation defines line $t$?

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

$y=13x-\\frac{1}{3}$

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

$y=9x+10$

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

$y=-\\frac{x}{3}+10$

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

$y=-\\frac{x}{3}+13$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-36"}

Line $t$ in the $xy$-plane has a slope of $-\frac{1}{3}$ and passes through the point $(9,10)$. Which equation defines line $t$?