which of the following is the graph of this function rule?
\y = \frac{3x}{2} - 5\

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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", "Graphical Identification" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "Graphical Identification" ] } ## Identify key parameters of the linear equation $$ \begin{aligned} &\text{Equation: } y = \frac{3}{2}x - 5 \ &\text{Slope } (m) = \frac{3}{2} \ &\text{y-intercept } (b) = -5 \implies (0, -5) \end{aligned} $$ ## Calculate a second point on the line $$ \begin{aligned} &\text{Let } x = 2 \ &y = \frac{3}{2}(2) - 5 = 3 - 5 = -2 \implies (2, -2) \end{aligned} $$ ## Match points with the given graphs $$ \begin{aligned} &\text{Graph 1 (Left): Passes through } (0, -5) \text{ and } (2, -2). \ &\text{Graph 2 (Middle): Passes through } (0, 0) \text{ and } (2, 3). \ &\text{Graph 3 (Right): Passes through } (0, 5) \text{ and } (-2, 2). \end{aligned} $$

(A) First graph (left) with y-intercept at (0, -5) and passing through (2, -2)

(B) Second graph (middle) with y-intercept at (0, 0) and passing through (2, 3)

(C) Third graph (right) with y-intercept at (0, 5) and passing through (-2, 2)

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "1.5*x - 5", "latex": "y = \frac{3}{2}x - 5" }, -3, 5 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [ [0, -5] ], "properties": { "name": "(0, -5)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [ [2, -2] ], "properties": { "name": "(2, -2)", "size": 4, "color": "#F2557F", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Functions" ] }

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Question

Explanation:

Identify key parameters of the linear equation

Calculate a second point on the line

Match points with the given graphs

Answer: