a direct variation function contains the points $(-9, -3)$ and $(-12, -4)$. which equation represents the function?

$y = -3x$

$y = -\frac{x}{3}$

$y = \frac{x}{3}$

$y = 3x$

Question

a direct variation function contains the points $(-9, -3)$ and $(-12, -4)$. which equation represents the function?

$y = -3x$

$y = -\frac{x}{3}$

$y = \frac{x}{3}$

$y = 3x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Direct Variation" ], "new_concepts": [], "current_concepts": [ "Direct Variation" ] } ## Set up the direct variation equation $$ y = kx $$ ## Solve for the constant of variation k $$ \begin{aligned} -3 &= k(-9) \ k &= \frac{-3}{-9} = \frac{1}{3} \end{aligned} $$ ## Write the final equation $$ y = \frac{1}{3}x = \frac{x}{3} $$

(A) $y = -3x$

(B) $y = -\frac{x}{3}$

(C) $y = \frac{x}{3}$

(D) $y = 3x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Direct Variation" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the direct variation equation

Solve for the constant of variation k

Write the final equation

Answer: