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

$x$	$-11$	$-10$	$-9$	$-8$
$f(x)$	$21$	$18$	$15$	$12$

The table above shows some values of $x$ and their corresponding values $f(x)$ for the linear function $f$. What is the $x$-intercept of the graph of $y=f(x)$ 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-166"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$x$	$-11$	$-10$	$-9$	$-8$
$f(x)$	$21$	$18$	$15$	$12$

The table above shows some values of $x$ and their corresponding values $f(x)$ for the linear function $f$. What is the $x$-intercept of the graph of $y=f(x)$ in the $xy$-plane?

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

Choice B is correct. The equation of a linear function can be written in the form $y=mx+b$, where $y=f(x)$, $m$ is the slope of the graph of $y=f(x)$, and $b$ is the $y$-coordinate of the $y$-intercept of the graph. The value of $m$ can be found using the slope formula, $m=\\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$. According to the table, the points $(-11,21)$ and $(-10,18)$ lie on the graph of $y=f(x)$. Using these two points in the slope formula yields $m=\\dfrac{18-21}{-10+11}$, or $-3$. Substituting $-3$ for $m$ in the slope-intercept form of the equation yields $y=-3x+b$. The value of $b$ can be found by substituting values from the table and solving; for example, substituting the coordinates of the point $(-11,21)$ into the equation $y=-3x+b$ gives $21=-3(-11)+b$, which yields $b=-12$. This means the function given by the table can be represented by the equation $y=-3x-12$. The value of the $x$-intercept of the graph of $y=f(x)$ can be determined by finding the value of $x$ when $y=0$. Substituting $y=0$ into $y=-3x-12$ yields $0=-3x-12$, or $x=-4$. This corresponds to the point $(-4,0)$.

Choice A is incorrect and may result from substituting the value of the slope for the $x$-coordinate of the $x$-intercept. Choice C is incorrect and may result from a calculation error. Choice D is incorrect and may result from substituting the $y$-coordinate of the $y$-intercept for the $x$-coordinate of the $x$-intercept.

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

$x$	$-11$	$-10$	$-9$	$-8$
$f(x)$	$21$	$18$	$15$	$12$

The table above shows some values of $x$ and their corresponding values $f(x)$ for the linear function $f$. What is the $x$-intercept of the graph of $y=f(x)$ in the $xy$-plane?

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

$(-3,0)$

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

$(-9,0)$

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

$(-12,0)$

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

$(-4,0)$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-166"}