what is the constant of variation, k, of the direct variation, $y = kx$, through $(5, 8)$?

$k = -\frac{8}{5}$

$k = -\frac{5}{8}$

$k = \frac{5}{8}$

$k = \frac{8}{5}$

Question

what is the constant of variation, k, of the direct variation, $y = kx$, through $(5, 8)$?

$k = -\frac{8}{5}$

$k = -\frac{5}{8}$

$k = \frac{5}{8}$

$k = \frac{8}{5}$

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" ] } ## Substitute the given coordinates into the direct variation equation $$ \begin{aligned} y &= kx \ (x, y) &= (5, 8) \ 8 &= k(5) \end{aligned} $$ ## Solve for the constant of variation k $$ \begin{aligned} k &= \frac{8}{5} \end{aligned} $$

(A) $k = -\frac{8}{5}$

(B) $k = -\frac{5}{8}$

(C) $k = \frac{5}{8}$

(D) $k = \frac{8}{5}$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Substitute the given coordinates into the direct variation equation

Solve for the constant of variation k

Answer: