find the equation of the line that is perpendicular to $y = 6x - 2$ and contains the point $(6,-2)$.

\y = -\frac{?}{\box}x + \box\

Question

find the equation of the line that is perpendicular to $y = 6x - 2$ and contains the point $(6,-2)$.

\y = -\frac{?}{\box}x + \box\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Perpendicular Line Slopes" ], "current_concepts": [ "Slope-Intercept Form", "Perpendicular Line Slopes", "Point-Slope Form" ] } ## Find the slope of the perpendicular line $$ \begin{aligned} &m_1 = 6 \ &m_2 = -\frac{1}{m_1} = -\frac{1}{6} \end{aligned} $$ ## Solve for the y-intercept $$ \begin{aligned} &y = m_2 x + b \ &-2 = -\frac{1}{6}(6) + b \ &-2 = -1 + b \ &b = -1 \end{aligned} $$ ## Write the final equation $$ y = -\frac{1}{6}x - 1 $$ Find the equation of the line that is perpendicular to $y = 6x - 2$ and contains the point $(6,-2)$. $y = -\frac{\text{1}}{\text{6}}x + \text{-1}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Perpendicular Line Slopes" ] }

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QUESTION IMAGE

Question

Explanation:

Find the slope of the perpendicular line

Solve for the y-intercept

Write the final equation

Answer: