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

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Coordinate Plane", "Ordered Pairs", "Linear Equations" ], "new_concepts": [ "Graphing Linear Equations", "Slope-Intercept Form" ], "current_concepts": [ "Coordinate Plane", "Ordered Pairs", "Linear Equations", "Graphing Linear Equations", "Slope-Intercept Form" ] } ## Identify the y-intercept Using the *Linear Equations* knowledge point $$ \begin{aligned} &y = -2x + 3\ &\text{For } x = 0:\ &y = 3 - 2(0) = 3\ &\text{The } y\text{-intercept is } (0, 3). \end{aligned} $$ ## Calculate key ordered pairs Using the *Ordered Pairs* and *Coordinate Plane* knowledge points $$ \begin{aligned} &\text{For } x = 1:\ &y = 3 - 2(1) = 1 \implies (1, 1)\ &\text{For } x = 2:\ &y = 3 - 2(2) = -1 \implies (2, -1) \end{aligned} $$ ## Match points to the correct graph Using the *Coordinate Plane* knowledge point $$ \begin{aligned} &\text{Graph 1 (Left): Passes through } (0, 3), (1, 1), \text{ and } (2, -1).\ &\text{Graph 2 (Middle): Passes through } (-2, 1), (-1, -1), \text{ and } (0, -3).\ &\text{Graph 3 (Right): Passes through } (0, 3), (-1, 1), \text{ and } (-2, -1).\ &\text{Therefore, the first graph is correct.} \end{aligned} $$

(A) The first graph (left), passing through (0, 3), (1, 1), and (2, -1)

(B) The second graph (middle), passing through (-2, 1), (-1, -1), and (0, -3)

(C) The third graph (right), passing through (0, 3), (-1, 1), and (-2, -1)

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "3 - 2*x", "latex": "y = 3 - 2x" }, -2, 4 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [ [0, 3] ], "properties": { "name": "(0, 3)", "size": 4, "color": "#5583F2", "withLabel": true } }, { "type": "point", "params": [ [1, 1] ], "properties": { "name": "(1, 1)", "size": 4, "color": "#5583F2", "withLabel": true } }, { "type": "point", "params": [ [2, -1] ], "properties": { "name": "(2, -1)", "size": 4, "color": "#5583F2", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

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Question

Explanation:

Identify the y-intercept

Calculate key ordered pairs

Match points to the correct graph

Answer: