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

Line $k$ is defined by $y=3x+15$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

","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-5"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

Line $k$ is defined by $y=3x+15$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

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

Choice A is correct. It's given that line $j$ is perpendicular to line $k$ in the $xy$-plane. It follows that the slope of line $j$ is the opposite reciprocal of the slope of line $k$. The equation for line $k$ is written in slope-intercept form $y=mx+b$, where $m$ is the slope of the line and $b$ is the $y$-coordinate of the $y$-intercept of the line. It follows that the slope of line $k$ is $3$. The opposite reciprocal of a number is $-1$ divided by the number. Thus, the opposite reciprocal of $3$ is $-\\frac{1}{3}$. Therefore, the slope of line $j$ is $-\\frac{1}{3}$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.
\"\"\"

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

Line $k$ is defined by $y=3x+15$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

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

$-\\frac{1}{12}$

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

\$-\\frac{1}{18}\$

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

$-\\frac{1}{45}$

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

$-\\frac{1}{3}$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-5"}