\y = -\frac{1}{9}x + 10\

click to select points on the graph.

Question

\y = -\frac{1}{9}x + 10\

click to select points on the graph.

Accepted Answer

{ "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 the y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = mx + b \implies y = -\frac{1}{9}x + 10\ &b = 10 \implies (0, 10) \end{aligned} $$ ## Find a second point using the slope Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &m = \frac{\text{rise}}{\text{run}} = \frac{-1}{9}\ &x = -9 \implies y = -\frac{1}{9}(-9) + 10 = 11 \quad (\text{off-grid})\ &x = -9 \text{ is outside standard grid, let's check } x = -9 \text{ on the graph: } (-9, 11)\ &x = 0 \implies (0, 10)\ &\text{Since the grid x-axis goes from } -10 \text{ to } 8\text{, we can use } (-9, 11) \text{ or find another integer point if possible.} \end{aligned} $$ To graph the equation $y = -\frac{1}{9}x + 10$, plot the following two points on the coordinate plane: * **First point (y-intercept):** $(0, 10)$ * **Second point:** $(-9, 11)$ { "elements": [ { "type": "point", "params": [[0, 10]], "properties": { "name": "(0, 10)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-9, 11]], "properties": { "name": "(-9, 11)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, 10], [-9, 11]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the y-intercept

Find a second point using the slope

Answer: