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

In the $xy$-plane, the graph of the linear function $\\bm{f}$ contains the points $(0,2)$ and $(8,34)$. Which equation defines $\\bm{f}$, where $y=f(\\bm{x})$?

","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-69"}],"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 $\\bm{f}$ contains the points $(0,2)$ and $(8,34)$. Which equation defines $\\bm{f}$, where $y=f(\\bm{x})$?

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

Choice C is correct. In the $xy$-plane, 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 $\\bm{y}=\\bm{f}(\\bm{x})$. It's given that the graph of the linear function $\\bm{f}$, where $\\bm{y}=\\bm{f}(\\bm{x})$, in the $xy$-plane contains the point $(0,2)$. Thus, $b=2$. The slope of the graph of a line containing any two points $(x_1,y_1)$ and $(x_2,y_2)$ 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 $(0,2)$ and $(8,34)$, it follows that the slope of the graph of the line containing these points is $m=\\frac{34-2}{8-0}$, or $m=4$. Substituting 4 for $m$ and 2 for $b$ in $f(x)=mx+b$ yields $f(x)=4x+2$.

Choice A is incorrect. This function represents a graph with a slope of 2 and a y-intercept of $(0,42)$.

Choice B is incorrect. This function represents a graph with a slope of 32 and a y-intercept of $(0,36)$.

Choice D is incorrect. This function represents a graph with a slope of 8 and a y-intercept of $(0,2)$.

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

In the $xy$-plane, the graph of the linear function $\\bm{f}$ contains the points $(0,2)$ and $(8,34)$. Which equation defines $\\bm{f}$, where $y=f(\\bm{x})$?

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

$f(\\bm{x})=2x+42$

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

$f(\\bm{x})=32x+36$

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

$f(\\bm{x})=8x+2$

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

$f(\\bm{x})=4x+2$

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

Choice A is incorrect. This function represents a graph with a slope of 2 and a y-intercept of $(0,42)$.

Choice B is incorrect. This function represents a graph with a slope of 32 and a y-intercept of $(0,36)$.

Choice D is incorrect. This function represents a graph with a slope of 8 and a y-intercept of $(0,2)$.

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

Choice A is incorrect. This function represents a graph with a slope of 2 and a y-intercept of $(0,42)$.

Choice B is incorrect. This function represents a graph with a slope of 32 and a y-intercept of $(0,36)$.

Choice D is incorrect. This function represents a graph with a slope of 8 and a y-intercept of $(0,2)$.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-69"}

In the $xy$-plane, the graph of the linear function $\bm{f}$ contains the points $(0,2)$ and $(8,34)$. Which equation defines $\bm{f}$, where $y=f(\bm{x})$?