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

The point with coordinates $(d,4)$ lies on the line shown. What is the value of $d$?

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","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-258"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

The point with coordinates $(d,4)$ lies on the line shown. What is the value of $d$?

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

Choice C is correct. It's given from the graph that the points $(0,7)$ and $(8,0)$ lie on the line. For two points on a line, $(x_{1},y_{1})$ and $(x_{2},y_{2})$, the slope of the line can be calculated using the slope formula $m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. Substituting $(0,7)$ for $(x_{1},y_{1})$ and $(8,0)$ for $(x_{2},y_{2})$ in this formula, the slope of the line can be calculated as $m=\\frac{0-7}{8-0}$, or $m=-\\frac{7}{8}$. It's also given that the point $(d,4)$ lies on the line. Substituting $(d,4)$ for $(x_{1}, y_{1})$, $(8,0)$ for $(x_{2}, y_{2})$, and $-\\frac{7}{8}$ for $m$ in the slope formula yields $-\\frac{7}{8}=\\frac{0-4}{8-d}$, or $-\\frac{7}{8}=\\frac{-4}{8-d}$. Multiplying both sides of this equation by $8-d$ yields $-\\frac{7}{8}(8-d)=-4$. Expanding the left-hand side of this equation yields $-7+\\frac{7}{8}d=-4$. Adding $7$ to both sides of this equation yields $\\frac{7}{8}d=3$. Multiplying both sides of this equation by $\\frac{8}{7}$ yields $d=\\frac{24}{7}$. Thus, the value of $d$ is $\\frac{24}{7}$.

Choice A is incorrect. This is the value of $y$ when $x=4$.

Choice B 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":"

The point with coordinates $(d,4)$ lies on the line shown. What is the value of $d$?

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

$\\dfrac{7}{2}$

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

$\\dfrac{26}{7}$

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

$\\dfrac{27}{8}$

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

$\\dfrac{24}{7}$

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

Choice A is incorrect. This is the value of $y$ when $x=4$.

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

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

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

Choice A is incorrect. This is the value of $y$ when $x=4$.

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-258"}