which graph matches this direct variation equation?
\y = -4x\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "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 $$ \begin{aligned} &y = -4x \ &\text{Slope } (m) = -4 \ &\text{y-intercept } (b) = 0 \end{aligned} $$ ## Determine key points on the graph $$ \begin{aligned} &(x, y) = (0, 0) \ &(x, y) = (-1, 4) \ &(x, y) = (1, -4) \end{aligned} $$ ## Match with the given graph options $$ \begin{aligned} &\text{Graph 1 (Left): Passes through } (0,0) \text{ and } (4, -1) \implies m = -\frac{1}{4} \ &\text{Graph 2 (Middle): Passes through } (0,0) \text{ and } (-1, 4) \implies m = -4 \ &\text{Graph 3 (Right): Passes through } (0,0) \text{ and } (1, 4) \implies m = 4 \end{aligned} $$

(A) Left graph (slope of $-\frac{1}{4}$)

(B) Middle graph (slope of $-4$)

(C) Right graph (slope of $4$)

{ "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "O", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-1, 4]], "properties": { "name": "A", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-4*x", "latex": "y = -4x"}, -3, 3], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Direct Variation" ] }

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Question

Explanation:

Identify the slope and y-intercept

Determine key points on the graph

Match with the given graph options

Answer: