find the graph of this linear function:
\y = \frac{1}{4}x - 2\

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 $$ \begin{aligned} &y = mx + b \implies y = \frac{1}{4}x - 2 \ &\text{y-intercept } (0, b) = (0, -2) \ &\text{slope } m = \frac{1}{4} \end{aligned} $$ ## Find a second point on the line $$ \begin{aligned} &x = 4 \implies y = \frac{1}{4}(4) - 2 = 1 - 2 = -1 \ &\text{Point: } (4, -1) \end{aligned} $$ ## Match with the given graphs $$ \begin{aligned} &\text{Graph 1 (Left): Passes through } (0, -3) \text{ and } (4, -2) \implies y = \frac{1}{4}x - 3 \ &\text{Graph 2 (Middle): Passes through } (0, -2), (2, -1), (4, 0) \implies y = \frac{1}{2}x - 2 \ &\text{Graph 3 (Right): Passes through } (0, -2) \text{ and } (4, -1) \implies y = \frac{1}{4}x - 2 \end{aligned} $$

(A) Left graph

(B) Middle graph

(C) Right graph

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "0.25*x - 2", "latex": "y = \frac{1}{4}x - 2" }, -3, 7 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [ [0, -2] ], "properties": { "name": "(0, -2)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [ [4, -1] ], "properties": { "name": "(4, -1)", "size": 4, "color": "#F2557F", "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 and slope

Find a second point on the line

Match with the given graphs

Answer: