which direct variation equation goes through the point $(4, 24)$?

$y = \frac{1}{3}x$

$y = 12x$

$y = 4x$

$y = 6x$

Question

which direct variation equation goes through the point $(4, 24)$?

$y = \frac{1}{3}x$

$y = 12x$

$y = 4x$

$y = 6x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Direct Variation" ], "new_concepts": [], "current_concepts": [ "Direct Variation", "Linear Equations" ] } ## Identify the direct variation formula Using the *Direct Variation* knowledge point $$ y = kx $$ ## Substitute the given point to find the constant of variation Using the *Direct Variation* knowledge point $$ \begin{aligned} (x, y) &= (4, 24) \ 24 &= k(4) \ k &= \frac{24}{4} \ k &= 6 \end{aligned} $$ ## Write the final direct variation equation Using the *Direct Variation* knowledge point $$ y = 6x $$

(A) $y = \frac{1}{3}x$

(B) $y = 12x$

(C) $y = 4x$

(D) $y = 6x$

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

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QUESTION IMAGE

Question

Explanation:

Identify the direct variation formula

Substitute the given point to find the constant of variation

Write the final direct variation equation

Answer: