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

In the linear function $h$, $h(0)=41$ and $h(1)=40$. Which equation defines $h$?

","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-182"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

In the linear function $h$, $h(0)=41$ and $h(1)=40$. Which equation defines $h$?

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

Choice A is correct. An equation defining a linear function can be written in the form $h(x)=ax+b$, where $a$ and $b$ are constants. It's given that $h(0)=41$ Substituting $0$ for $x$ and $41$ for $h(x)$ in the equation $h(x)=ax+b$ yields $41=a(0)+b$, or $b=41$ Substituting $41$ for $b$ in the equation $h(x)=ax+b$ yields $h(x)=ax+41$ It's also given that $h(1)=40$ Substituting $1$ for $x$ and $40$ for $h(x)$ in the equation $h(x)=ax+41$ yields $40=a(1)+41$, or $40=a+41$ Subtracting $41$ from the left- and right-hand sides of this equation yields $-1=a$ Substituting $-1$ for $a$ in the equation $h(x)=ax+41$ yields $h(x)=-1x+41$, or $h(x)=-x+41$

Choice B is incorrect. Substituting $0$ for $x$ and $41$ for $h(x)$ in this equation yields $41=-0$, which isn't a true statement.

Choice C is incorrect. Substituting $0$ for $x$ and $41$ for $h(x)$ in this equation yields $41=-41(0)$, or $41=0$, which isn't a true statement.

Choice D is incorrect. Substituting $41$ for $h(x)$ in this equation yields $41=-41$, which isn't a true statement.

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

In the linear function $h$, $h(0)=41$ and $h(1)=40$. Which equation defines $h$?

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

$h(x)=-x$

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

$h(x)=-41x$

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

$h(x)=-41$

"}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$h(x)=-x+41$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-182"}