which graph matches this direct variation equation?
\y = -2x\

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", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Direct Variation", "Graphing Linear Equations", "Slope Formula" ] } ## Identify key features of the equation $$ \begin{aligned} &y = -2x \ &\text{Slope } (m) = -2 \ &\text{y-intercept } (b) = 0 \end{aligned} $$ ## Determine points on the graph $$ \begin{aligned} &x = 0 \implies y = 0 \quad (0,0) \ &x = 1 \implies y = -2 \quad (1,-2) \ &x = -1 \implies y = 2 \quad (-1,2) \end{aligned} $$ ## Match points with the given options $$ \begin{aligned} &\text{Graph 1 (Left): passes through } (0,0), (-1,2), (1,-2) \ &\text{Graph 2 (Middle): passes through } (0,0), (1,2), (-1,-2) \ &\text{Graph 3 (Right): passes through } (0,0), (-1,3), (1,-3) \end{aligned} $$

(A) The first graph (left) with points at (-1, 2), (0, 0), and (1, -2)

(B) The second graph (middle) with points at (1, 2), (0, 0), and (-1, -2)

(C) The third graph (right) with points at (-1, 3), (0, 0), and (1, -3)

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "-2*x", "latex": "y = -2x" }, -5, 5 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y = -2x", "withLabel": true } }, { "type": "point", "params": [ [0, 0] ], "properties": { "name": "(0,0)", "size": 4, "color": "#5583F2", "strokeColor": "#5583F2", "withLabel": true } }, { "type": "point", "params": [ [-1, 2] ], "properties": { "name": "(-1,2)", "size": 4, "color": "#5583F2", "strokeColor": "#5583F2", "withLabel": true } }, { "type": "point", "params": [ [1, -2] ], "properties": { "name": "(1,-2)", "size": 4, "color": "#5583F2", "strokeColor": "#5583F2", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

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Question

Explanation:

Identify key features of the equation

Determine points on the graph

Match points with the given options

Answer: