what is the constant of variation, (k), of the line (y=kx) through ((3,18)) and ((5,30))?

* (\frac{3}{5})
* (\frac{5}{3})
* 3
* 6

Question

what is the constant of variation, (k), of the line (y=kx) through ((3,18)) and ((5,30))?

* (\frac{3}{5})
* (\frac{5}{3})
* 3
* 6

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", "Linear Rate of Change" ] } ## Substitute a given point into the direct variation equation $$ \begin{aligned} &y = kx \ &\text{Using } (x, y) = (3, 18): \ &18 = k(3) \end{aligned} $$ ## Solve for the constant of variation $$ \begin{aligned} &k = \frac{18}{3} \ &k = 6 \end{aligned} $$ ## Verify with the second given point $$ \begin{aligned} &\text{Using } (x, y) = (5, 30): \ &30 = 6(5) \ &30 = 30 \end{aligned} $$

(A) $\frac{3}{5}$

(B) $\frac{5}{3}$

(C) 3

(D) 6

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

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QUESTION IMAGE

Question

Explanation:

Substitute a given point into the direct variation equation

Solve for the constant of variation

Verify with the second given point

Answer: