10. $y = -x$

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10. $y = -x$

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Graphing Linear Equations" ] } ## Identify slope and intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = mx + b \ &y = -1x + 0 \ &m = -1, \quad b = 0 \end{aligned} $$ ## Find key coordinate points Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &\text{If } x = 0 \implies y = 0 \implies (0, 0) \ &\text{If } x = 1 \implies y = -1 \implies (1, -1) \ &\text{If } x = -1 \implies y = 1 \implies (-1, 1) \end{aligned} $$ To graph the linear equation $y = -x$, plot the y-intercept at the origin $(0, 0)$. Since the slope is $-1$, move down 1 unit and right 1 unit to plot a second point at $(1, -1)$, then draw a straight line passing through these points. { "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "Origin (0,0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, -1]], "properties": { "name": "(1,-1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-x", "latex": "y = -x"}, -10, 10], "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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Identify slope and intercept

Find key coordinate points

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