which graph matches this direct variation equation?
\y = -\frac{3}{4}x\

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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", "Slope-Intercept Form", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Direct Variation", "Slope-Intercept Form", "Graphing Linear Equations" ] } ## Identify the y-intercept of the direct variation equation $$ y = -\frac{3}{4}x \implies \text{y-intercept} = (0,0) $$ ## Determine the slope and a second point on the line $$ \begin{aligned} m &= -\frac{3}{4} \ (x, y) &= (4, -3) \end{aligned} $$ ## Match with the given graphs $$ \begin{aligned} &\text{Graph 1: Passes through } (0, 2) \quad (\text{Incorrect}) \ &\text{Graph 2: Passes through } (0, 0) \text{ and } (4, -3) \quad (\text{Correct}) \ &\text{Graph 3: Passes through } (0, 0) \text{ and } (4, 3) \quad (\text{Incorrect}) \end{aligned} $$

(A) Graph 1: Line passing through (0, 2) and (4, -1)

(B) Graph 2: Line passing through (0, 0) and (4, -3)

(C) Graph 3: Line passing through (0, 0) and (4, 3)

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

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Question

Explanation:

Identify the y-intercept of the direct variation equation

Determine the slope and a second point on the line

Match with the given graphs

Answer: