question 8 (1 point)

which graph matches the equation $y = -3/4x + 2$?

Question

question 8 (1 point)

which graph matches the equation $y = -3/4x + 2$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Graphing Linear Equations" ] } ## Identify the y-intercept and slope $$ \begin{aligned} &y = -\frac{3}{4}x + 2 \ &\text{y-intercept: } (0, 2) \ &\text{slope } (m): -\frac{3}{4} \end{aligned} $$ ## Find a second point on the line $$ \begin{aligned} &x = 4 \ &y = -\frac{3}{4}(4) + 2 = -3 + 2 = -1 \ &\text{Point: } (4, -1) \end{aligned} $$ ## Match with the correct graph $$ \begin{aligned} &\text{Graph 1: Passes through } (0, 2) \text{ and } (4, 5) \implies m = \frac{3}{4} \ &\text{Graph 2: Horizontal line } y = 2 \implies m = 0 \ &\text{Graph 3: Passes through } (0, 2) \text{ and } (4, -1) \implies m = -\frac{3}{4} \end{aligned} $$

(A) Graph with a positive slope passing through (0, 2) and (4, 5)

(B) Graph of a horizontal line at y = 2

(C) Graph with a negative slope passing through (0, 2) and (4, -1)

{ "elements": [ { "type": "point", "params": [[0, 2]], "properties": { "name": "(0, 2)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[4, -1]], "properties": { "name": "(4, -1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, 2], [4, -1]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the y-intercept and slope

Find a second point on the line

Match with the correct graph

Answer: