use your knowledge of $x$- and $y$-intercepts to choose the correct graph of the equation.

\3x - 2y = 6\

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b
c
d

Question

use your knowledge of $x$- and $y$-intercepts to choose the correct graph of the equation.

\3x - 2y = 6\

a
b
c
d

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": [ "Intercepts of a Line", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Intercepts of a Line", "Graphing Linear Equations", "Linear Equations in Two Variables" ] } ## Find the x-intercept Using the *Intercepts of a Line* knowledge point $$ \begin{aligned} &3x - 2(0) = 6 \ &3x = 6 \ &x = 2 \implies (2, 0) \end{aligned} $$ ## Find the y-intercept Using the *Intercepts of a Line* knowledge point $$ \begin{aligned} &3(0) - 2y = 6 \ &-2y = 6 \ &y = -3 \implies (0, -3) \end{aligned} $$ ## Match the intercepts to the correct graph Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &\text{Graph a: } x\text{-intercept } (2,0), y\text{-intercept } (0,3) \ &\text{Graph b: } x\text{-intercept } (-2,0), y\text{-intercept } (0,-3) \ &\text{Graph c: } x\text{-intercept } (-2,0), y\text{-intercept } (0,3) \ &\text{Graph d: } x\text{-intercept } (2,0), y\text{-intercept } (0,-3) \end{aligned} $$

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b

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d

{ "elements": [ { "type": "point", "params": [[2, 0]], "properties": { "name": "(2, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, -3]], "properties": { "name": "(0, -3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[2, 0], [0, -3]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Intercepts of a Line" ] }

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QUESTION IMAGE

Question

Explanation:

Find the x-intercept

Find the y-intercept

Match the intercepts to the correct graph

Answer: