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

Line $p$ is defined by $2y+18x=9$. Line $r$ is perpendicular to line $p$ in the $xy$-plane. What is the slope of line $r$?

","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-11"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

Line $p$ is defined by $2y+18x=9$. Line $r$ is perpendicular to line $p$ in the $xy$-plane. What is the slope of line $r$?

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

Choice C is correct. It's given that line $r$ is perpendicular to line $p$ in the $xy$-plane. This means that the slope of line $r$ is the negative reciprocal of the slope of line $p$. If the equation for line $p$ is rewritten in slope-intercept form $y=mx+b$, where $m$ and $b$ are constants, then $m$ is the slope of the line and $(0,b)$ is its $y$-intercept. Subtracting $18x$ from both sides of the equation $2y+18x=9$ yields $2y=-18x+9$. Dividing both sides of this equation by $2$ yields $y=-9x+\\frac{9}{2}$. It follows that the slope of line $p$ is $-9$. The negative reciprocal of a number is $-1$ divided by the number. Therefore, the negative reciprocal of $-9$ is $\\frac{-1}{-9}$, or $\\frac{1}{9}$. Thus, the slope of line $r$ is $\\frac{1}{9}$.

Choice A is incorrect. This is the slope of line $p$, not line $r$.

Choice B is incorrect. This is the reciprocal, not the negative reciprocal, of the slope of line $p$.

Choice D is incorrect. This is the negative, not the negative reciprocal, of the slope of line $p$.

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

Line $p$ is defined by $2y+18x=9$. Line $r$ is perpendicular to line $p$ in the $xy$-plane. What is the slope of line $r$?

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

$-9$

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

$-\\frac{1}{9}$

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

$9$

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

\$\\frac{1}{9}\$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-11"}