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

For the function $f$, the graph of $y=f(x)$ in the $xy$-plane has a slope of $3$ and passes through the point $(0,-8)$. Which equation defines $f$?

","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-103"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

For the function $f$, the graph of $y=f(x)$ in the $xy$-plane has a slope of $3$ and passes through the point $(0,-8)$. Which equation defines $f$?

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

Choice B is correct. An equation defining a linear function can be written in the form $\\bm{f}(\\bm{x})=\\bm{m}\\bm{x}+b$, where $\\bm{m}$ and $b$ are constants, $m$ is the slope of the graph of $y=\\bm{f}(\\bm{x})$ in the $xy$-plane, and $(0,b)$ is the $y$-intercept of the graph. It's given that for the function $\\bm{f}$, the graph of $y=\\bm{f}(\\bm{x})$ in the $xy$-plane has a slope of $3$. Therefore, $\\bm{m}=3$It's also given that this graph passes through the point $(0,-8)$. Therefore, the $y$-intercept of the graph is $(0,-8)$, and it follows that $\\bm{b}=-8$. Substituting $3$ for $\\bm{m}$ and $-8$ for $\\bm{b}$ in the equation $\\bm{f}(\\bm{x})=mx+b$ yields $\\bm{f}(\\bm{x})=3\\bm{x}-8$. Thus, the equation that defines $\\bm{f}$ is $\\bm{f}(\\bm{x})=3\\bm{x}-8$.

Choice A is incorrect. For this function, the graph of $y=f(x)$ in the $xy$-plane passes through the point $(0,0)$, not $(0,-8)$

Choice C is incorrect. For this function, the graph of $y=f(x)$ in the $xy$-plane passes through the point $(0,5)$, not $(0,-8)$

Choice D is incorrect. For this function, the graph of $y=f(x)$ in the $xy$-plane passes through the point $(0,11)$, not $(0,-8)$

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

For the function $f$, the graph of $y=f(x)$ in the $xy$-plane has a slope of $3$ and passes through the point $(0,-8)$. Which equation defines $f$?

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

$f(x)=3x$

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

$f(x)=3x+5$

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

$f(x)=3x+11$

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

$f(x)=3x-8$

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

Choice C is incorrect. For this function, the graph of $y=f(x)$ in the $xy$-plane passes through the point $(0,5)$, not $(0,-8)$

Choice D is incorrect. For this function, the graph of $y=f(x)$ in the $xy$-plane passes through the point $(0,11)$, not $(0,-8)$

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

Choice C is incorrect. For this function, the graph of $y=f(x)$ in the $xy$-plane passes through the point $(0,5)$, not $(0,-8)$

Choice D is incorrect. For this function, the graph of $y=f(x)$ in the $xy$-plane passes through the point $(0,11)$, not $(0,-8)$

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-103"}