\\frac{-1}{3}x - \frac{1}{2}y = 1\

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Intercepts", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Linear Intercepts", "Graphing Linear Equations" ] } ## Find the x-intercept $$ \begin{aligned} &y = 0 \ &\frac{-1}{3}x - \frac{1}{2}(0) = 1 \ &-\frac{1}{3}x = 1 \ &x = -3 \ &\text{Intercept: } (-3, 0) \end{aligned} $$ ## Find the y-intercept $$ \begin{aligned} &x = 0 \ &\frac{-1}{3}(0) - \frac{1}{2}y = 1 \ &-\frac{1}{2}y = 1 \ &y = -2 \ &\text{Intercept: } (0, -2) \end{aligned} $$ ## Determine the line equation in slope-intercept form $$ \begin{aligned} &-\frac{1}{2}y = \frac{1}{3}x + 1 \ &y = -\frac{2}{3}x - 2 \end{aligned} $$ The line passes through the intercepts $(-3, 0)$ and $(0, -2)$. Its equation is $y = -\frac{2}{3}x - 2$. { "elements": [ { "type": "point", "params": [[-3, 0]], "properties": { "name": "(-3, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, -2]], "properties": { "name": "(0, -2)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[-3, 0], [0, -2]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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Find the x-intercept

Find the y-intercept

Determine the line equation in slope-intercept form

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