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

In the $xy$-plane, the graph of the linear function $f$ contains the points $(0,3)$ and $(7,31)$. Which equation defines $f$, where $y=f(x)$?

","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-17"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

In the $xy$-plane, the graph of the linear function $f$ contains the points $(0,3)$ and $(7,31)$. Which equation defines $f$, where $y=f(x)$?

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

Choice C is correct. In the $xy$-plane, an equation of the graph of a linear function can be written in the form $\\bm{f}(\\bm{x})=m\\bm{x}+b$, where $m$ represents the slope and $(0,b)$ represents the $y$-intercept of the graph of $\\bm{y}=f(\\bm{x})$. It's given that the graph of the linear function $f$, where $\\bm{y}=f(\\bm{x})$, in the $xy$-plane contains the point $(0,3)$. Thus, $b=3$. The slope of the graph of a line containing any two points $(\\bm{x}_{1},\\bm{y}_{1})$ and $(\\bm{x}_{2},\\bm{y}_{2})$ can be found using the slope formula, $m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. Since it's given that the graph of the linear function $f$ contains the points $(0.3)$ and $(7,31)$, it follows that the slope of the graph of the line containing these points is $m=\\frac{31-3}{7-0}$, or $m=4$. Substituting $4$ for $m$ and $3$ for $b$ in $f(x)=mx+b$ yields $f(x)=4x+3$.

Choice A is incorrect. This function represents a graph with a slope of $28$ and a $y$-intercept of $(0,34)$.

Choice B is incorrect. This function represents a graph with a slope of $3$ and a $y$-intercept of $(0,38)$.

Choice D is incorrect. This function represents a graph with a slope of $7$ and a $y$-intercept of $(0,3)$.

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

In the $xy$-plane, the graph of the linear function $f$ contains the points $(0,3)$ and $(7,31)$. Which equation defines $f$, where $y=f(x)$?

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

$f(x)=28x+34$

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

$f(x)=3x+38$

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

$f(x)=7x+3$

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

$f(x)=4x+3$

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

Choice A is incorrect. This function represents a graph with a slope of $28$ and a $y$-intercept of $(0,34)$.

Choice B is incorrect. This function represents a graph with a slope of $3$ and a $y$-intercept of $(0,38)$.

Choice D is incorrect. This function represents a graph with a slope of $7$ and a $y$-intercept of $(0,3)$.

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

Choice A is incorrect. This function represents a graph with a slope of $28$ and a $y$-intercept of $(0,34)$.

Choice B is incorrect. This function represents a graph with a slope of $3$ and a $y$-intercept of $(0,38)$.

Choice D is incorrect. This function represents a graph with a slope of $7$ and a $y$-intercept of $(0,3)$.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-17"}