find the equation of the line that is perpendicular to $y = -\frac{1}{5}x - 3$ and contains the point $(1,2)$.

$y = ?x + \square$

Question

find the equation of the line that is perpendicular to $y = -\frac{1}{5}x - 3$ and contains the point $(1,2)$.

$y = ?x + \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Linear Equations" ], "new_concepts": [ "Perpendicular Slopes" ], "current_concepts": [ "Slope-Intercept Form", "Linear Equations", "Perpendicular Slopes" ] } ## Find the perpendicular slope Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &m_1 = -\frac{1}{5}\ &m_2 = -\frac{1}{m_1} = -\frac{1}{-\frac{1}{5}} = 5 \end{aligned} $$ ## Solve for the y-intercept Using the *Linear Equations* knowledge point $$ \begin{aligned} &y = m_2 x + b\ &2 = 5(1) + b\ &b = 2 - 5 = -3 \end{aligned} $$ ## Write the final equation Using the *Slope-Intercept Form* knowledge point $$ y = 5x - 3 $$ Find the equation of the line that is perpendicular to $y = -\frac{1}{5}x - 3$ and contains the point $(1,2)$. $y =$ $5$$x +$ $-3$ { "elements": [ { "type": "functiongraph", "params": [{"js": "-0.2*x - 3", "latex": "y = -\frac{1}{5}x - 3"}, -10, 10], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "y = -1/5x - 3", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "5*x - 3", "latex": "y = 5x - 3"}, -10, 10], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "y = 5x - 3", "withLabel": true } }, { "type": "point", "params": [[1, 2]], "properties": { "name": "(1,2)", "size": 4, "color": "#8C55F2", "strokeColor": "#8C55F2", "fillColor": "#8C55F2", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Slopes" ] }

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QUESTION IMAGE

Question

Explanation:

Find the perpendicular slope

Solve for the y-intercept

Write the final equation

Answer: