graph $5x + 3y = 15$.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Graphing Linear Equations", "Intercept Method" ], "current_concepts": [ "Graphing Linear Equations", "Intercept Method" ] } ## Find the x-intercept $$ \begin{aligned} 5x + 3(0) &= 15 \ 5x &= 15 \ x &= 3 \implies (3, 0) \end{aligned} $$ ## Find the y-intercept $$ \begin{aligned} 5(0) + 3y &= 15 \ 3y &= 15 \ y &= 5 \implies (0, 5) \end{aligned} $$ ## Determine the line equation $$ y = -\frac{5}{3}x + 5 $$ To graph the linear equation $5x + 3y = 15$, plot the two intercepts and draw a straight line passing through them: * **$x$-intercept**: $(3, 0)$ * **$y$-intercept**: $(0, 5)$ { "elements": [ { "type": "point", "params": [[3, 0]], "properties": { "name": "(3, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, 5]], "properties": { "name": "(0, 5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[3, 0], [0, 5]], "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 line equation

Answer: