choose the graph of $y = -3x - 1$.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Functions", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "Slope-Intercept Form" ] } ## Identify the slope and y-intercept $$ \begin{aligned} &y = mx + b \ &m = -3 \ &b = -1 \end{aligned} $$ ## Determine key points on the line $$ \begin{aligned} &x = 0 \implies y = -1 \quad \text{Point: } (0, -1) \ &x = -1 \implies y = 2 \quad \text{Point: } (-1, 2) \ &x = 1 \implies y = -4 \quad \text{Point: } (1, -4) \end{aligned} $$ ## Match with the given graph options $$ \begin{aligned} &\text{Option 1: Positive slope (incorrect)} \ &\text{Option 2: Positive slope (incorrect)} \ &\text{Option 3: Negative slope, passes through } (0, -1) \text{ and } (-1, 2) \text{ (correct)} \end{aligned} $$

(A) Line with a steep positive slope passing near the origin

(B) Line with a shallow positive slope and a negative y-intercept

(C) Line with a steep negative slope passing through (0, -1)

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "-3*x - 1", "latex": "-3x - 1" }, -10, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [[0, -1]], "properties": { "name": "(0, -1)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[-1, 2]], "properties": { "name": "(-1, 2)", "size": 4, "color": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Linear Functions" ] }

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Question

Explanation:

Identify the slope and y-intercept

Determine key points on the line

Match with the given graph options

Answer: