\\frac{-1}{5}x + \frac{1}{5}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" ] } ## Convert the equation to slope-intercept form $$ \begin{aligned} \frac{-1}{5}x + \frac{1}{5}y &= -1 \ -x + y &= -5 \ y &= x - 5 \end{aligned} $$ ## Find the intercepts of the line $$ \begin{aligned} &\text{Let } x = 0 \implies y = -5 \quad \implies (0, -5) \ &\text{Let } y = 0 \implies x = 5 \quad \implies (5, 0) \end{aligned} $$ ## Determine the line equation for graphing $$ y = x - 5 $$ The equation of the line is $y = x - 5$, which passes through the $y$-intercept $(0, -5)$ and the $x$-intercept $(5, 0)$. { "elements": [ { "type": "point", "params": [[0, -5]], "properties": { "name": "(0, -5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[5, 0]], "properties": { "name": "(5, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, -5], [5, 0]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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Explanation:

Convert the equation to slope-intercept form

Find the intercepts of the line

Determine the line equation for graphing

Answer: