find the graph of this linear function:
\y = \frac{3}{2}x + 3\

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 $$ \begin{aligned} &y = mx + b \implies y = \frac{3}{2}x + 3 \ &\text{y-intercept } (0, b) = (0, 3) \ &\text{slope } m = \frac{3}{2} \end{aligned} $$ ## Find a second point on the line $$ \begin{aligned} &x = 2 \implies y = \frac{3}{2}(2) + 3 = 6 \implies (2, 6) \ &x = -2 \implies y = \frac{3}{2}(-2) + 3 = 0 \implies (-2, 0) \end{aligned} $$ ## Match with the given graphs $$ \begin{aligned} &\text{Graph 1: Negative slope, passes through } (0, 3) \text{ and } (3, 1) \ &\text{Graph 2: Positive slope, passes through } (0, 3), (2, 6), \text{ and } (-2, 0) \ &\text{Graph 3: Positive slope, passes through } (0, 3) \text{ and } (3, 5) \end{aligned} $$

(A) Left graph: line passing through (0, 3) and (3, 1)

(B) Middle graph: line passing through (-2, 0), (0, 3), and (2, 6)

(C) Right graph: line passing through (-3, 1), (0, 3), and (3, 5)

{ "elements": [ { "type": "point", "params": [[0, 3]], "properties": { "name": "(0, 3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-2, 0]], "properties": { "name": "(-2, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[2, 6]], "properties": { "name": "(2, 6)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "1.5*x + 3", "latex": "\frac{3}{2}x + 3"}, -6, 6], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "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: