graphing lines from equations

graph the line with the equation
\y = -\frac{1}{5}x + 7.\

Question

graphing lines from equations

graph the line with the equation
\y = -\frac{1}{5}x + 7.\

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 y-intercept $$ \begin{aligned} &y = -\frac{1}{5}x + 7\ &\text{y-intercept: } (0, 7) \end{aligned} $$ ## Find a second point using the slope $$ \begin{aligned} &m = -\frac{1}{5} = \frac{\text{rise}}{\text{run}}\ &(x_2, y_2) = (0 + 5, 7 - 1) = (5, 6) \end{aligned} $$ ## Determine the equation of the line $$ y = -\frac{1}{5}x + 7 $$ To graph the line with the equation $y = -\frac{1}{5}x + 7$, plot the y-intercept at $(0, 7)$. From there, use the slope $m = -\frac{1}{5}$ by moving down 1 unit and right 5 units to plot a second point at $(5, 6)$. Draw a straight line passing through both points. { "elements": [ { "type": "point", "params": [[0, 7]], "properties": { "name": "(0, 7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[5, 6]], "properties": { "name": "(5, 6)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, 7], [5, 6]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

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Question

Explanation:

Identify the y-intercept

Find a second point using the slope

Determine the equation of the line

Answer: