find the graph of this linear function:
\y = -4x + 2\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Graphing Linear Equations", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Graphing Linear Equations", "Slope-Intercept Form" ] } ## Identify the y-intercept and slope $$ \begin{aligned} &y = mx + b \implies y = -4x + 2 \ &\text{y-intercept } (0, b) = (0, 2) \ &\text{slope } m = -4 \end{aligned} $$ ## Find a second point on the line $$ \begin{aligned} &x = 1 \implies y = -4(1) + 2 = -2 \ &\text{Point: } (1, -2) \end{aligned} $$ ## Match with the given graphs $$ \begin{aligned} &\text{Graph 1 (Left): Passes through } (0, 2) \text{ and } (1, -2) \ &\text{Graph 2 (Middle): Passes through } (0, 2) \text{ and } (-1, -2) \implies m = 4 \ &\text{Graph 3 (Right): Passes through } (0, 2) \text{ and } (4, 1) \implies m = -\frac{1}{4} \end{aligned} $$

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

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

(C) The third graph (right) with points at (0, 2) and (4, 1)

{ "elements": [ { "type": "point", "params": [[0, 2]], "properties": { "name": "(0, 2)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, -2]], "properties": { "name": "(1, -2)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, 2], [1, -2]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } } ], "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 the y-intercept and slope

Find a second point on the line

Match with the given graphs

Answer: