when $x = 3$, $y = 16$ and when $x = 6$, $y = 8$. which inverse variation equation can be used to model this function?

$y = \frac{4}{3x}$
$y = 48x$
$y = \frac{4}{3}x$
$y = \frac{48}{x}$

Question

when $x = 3$, $y = 16$ and when $x = 6$, $y = 8$. which inverse variation equation can be used to model this function?

$y = \frac{4}{3x}$
$y = 48x$
$y = \frac{4}{3}x$
$y = \frac{48}{x}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Inverse Variation" ], "current_concepts": [ "Inverse Variation" ] } ## Set up the inverse variation equation $$ y = \frac{k}{x} $$ ## Solve for the constant of variation k $$ \begin{aligned} 16 &= \frac{k}{3} \ k &= 16 \cdot 3 \ k &= 48 \end{aligned} $$ ## Write the final equation $$ y = \frac{48}{x} $$

(A) $y = \frac{4}{3x}$

(B) $y = 48x$

(C) $y = \frac{4}{3}x$

(D) $y = \frac{48}{x}$

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

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QUESTION IMAGE

Question

Explanation:

Set up the inverse variation equation

Solve for the constant of variation k

Write the final equation

Answer: