which graph matches this direct variation equation?
\y = -3x\

Question

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 Direction", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Direct Variation", "Slope Direction", "Graphing Linear Equations" ] } ## Identify the slope and y-intercept $$ \begin{aligned} &y = mx + b \ &y = -3x \implies m = -3,\quad b = 0 \end{aligned} $$ ## Determine key points on the graph $$ \begin{aligned} &x = 0 \implies y = 0 \quad \text{Point: } (0, 0) \ &x = 1 \implies y = -3 \quad \text{Point: } (1, -3) \ &x = -1 \implies y = 3 \quad \text{Point: } (-1, 3) \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &\text{Graph 1 (Left): } m = 3 > 0 \quad \text{Passes through } (1, 3) \ &\text{Graph 2 (Middle): } m = -3 < 0 \quad \text{Passes through } (1, -3) \text{ and } (-1, 3) \ &\text{Graph 3 (Right): } m = -\frac{1}{3} \quad \text{Passes through } (3, -1) \end{aligned} $$

(A) Left graph (positive slope of 3)

(B) Middle graph (negative slope of -3)

(C) Right graph (negative slope of -1/3)

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

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QUESTION IMAGE

Question

Explanation:

Identify the slope and y-intercept

Determine key points on the graph

Match with the given options

Answer: