write an equation of the line perpendicular to the given line that contains p.

$p(9, -6)$; $y = \frac{1}{5}x + 4$

write an equation for the line in point-slope form.

(simplify your answer. use integers or fractions for any numbers in the equation.)

Question

write an equation of the line perpendicular to the given line that contains p.

$p(9, -6)$; $y = \frac{1}{5}x + 4$

write an equation for the line in point-slope form.

(simplify your answer. use integers or fractions for any numbers in the equation.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Lines", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Perpendicular Lines", "Point-Slope Form" ] } ## Find the perpendicular slope $$ \begin{aligned} &m_1 = \frac{1}{5} \ &m_2 = -\frac{1}{m_1} = -5 \end{aligned} $$ ## Substitute into point-slope form $$ \begin{aligned} &(x_1, y_1) = (9, -6) \ &y - y_1 = m_2(x - x_1) \ &y - (-6) = -5(x - 9) \ &y + 6 = -5(x - 9) \end{aligned} $$ Write an equation for the line in point-slope form. $y+6=-5(x-9)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Lines" ] }

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QUESTION IMAGE

Question

Explanation:

Find the perpendicular slope

Substitute into point-slope form

Answer: