graph the line.

(y = \frac{2}{5}x - 5)

Question

graph the line.

(y = \frac{2}{5}x - 5)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Graphing Linear Equations" ] } ## Identify the slope and y-intercept $$ \begin{aligned} &y = mx + b \implies y = \frac{2}{5}x - 5 \ &\text{Slope } (m) = \frac{2}{5} \ &\text{y-intercept } (b) = -5 \implies (0, -5) \end{aligned} $$ ## Determine a second point using the slope $$ \begin{aligned} &\text{Rise} = 2, \quad \text{Run} = 5 \ &(x_2, y_2) = (0 + 5, -5 + 2) = (5, -3) \end{aligned} $$ ## Write the equation of the line $$ y = \frac{2}{5}x - 5 $$ To graph the line $y = \frac{2}{5}x - 5$, plot the y-intercept at $(0, -5)$, and use the slope $\frac{2}{5}$ (rise 2, run 5) to plot a second point at $(5, -3)$, then draw a straight line through these points. { "elements": [ { "type": "point", "params": [[0, -5]], "properties": { "name": "(0, -5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[5, -3]], "properties": { "name": "(5, -3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, -5], [5, -3]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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Question

Explanation:

Identify the slope and y-intercept

Determine a second point using the slope

Write the equation of the line

Answer: