select the correct answer.

an inverse variation includes the point $(-8, -19)$. which point would also belong in this inverse variation?

$\bigcirc (-19, -8)$
$\bigcirc (-8, 19)$
$\bigcirc (-19, 8)$
$\bigcirc (8, -19)$

Question

select the correct answer.

an inverse variation includes the point $(-8, -19)$. which point would also belong in this inverse variation?

$\bigcirc (-19, -8)$
$\bigcirc (-8, 19)$
$\bigcirc (-19, 8)$
$\bigcirc (8, -19)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Variation" ], "new_concepts": [], "current_concepts": [ "Inverse Variation" ] } ## Determine the constant of variation $$ k = x \cdot y = (-8) \cdot (-19) = 152 $$ ## Test the given options for the same constant $$ \begin{aligned} &\text{Option 1: } (-19) \cdot (-8) = 152 \ &\text{Option 2: } (-8) \cdot 19 = -152 \ &\text{Option 3: } (-19) \cdot 8 = -152 \ &\text{Option 4: } 8 \cdot (-19) = -152 \end{aligned} $$ ## Identify the matching point $$ (-19, -8) \implies 152 = k $$

(A) $(-19, -8)$

(B) $(-8, 19)$

(C) $(-19, 8)$

(D) $(8, -19)$

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

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QUESTION IMAGE

Question

Explanation:

Determine the constant of variation

Test the given options for the same constant

Identify the matching point

Answer: