\-3x + 3y = -9\
step 1 of 2
click on the plane to place the first

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Intercepts" ], "new_concepts": [ "Graphing Linear Equations" ], "current_concepts": [ "Linear Intercepts", "Graphing Linear Equations" ] } ## Find the x-intercept $$ \begin{aligned} -3x + 3(0) &= -9 \ -3x &= -9 \ x &= 3 \implies (3, 0) \end{aligned} $$ ## Find the y-intercept $$ \begin{aligned} -3(0) + 3y &= -9 \ 3y &= -9 \ y &= -3 \implies (0, -3) \end{aligned} $$ ## Determine the equation of the line $$ \begin{aligned} 3y &= 3x - 9 \ y &= x - 3 \end{aligned} $$ To graph the linear equation $-3x + 3y = -9$, find two points on the line: * The $x$-intercept is at $(3, 0)$. * The $y$-intercept is at $(0, -3)$. { "elements": [ { "type": "point", "params": [[3, 0]], "properties": { "name": "(3, 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": [[3, 0], [0, -3]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

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Explanation:

Find the x-intercept

Find the y-intercept

Determine the equation of the line

Answer: