select the correct answer.

which equation represents the line that is perpendicular to (y = \frac{4}{5}x + 23) and passes through (-40,20)?

(y = -\frac{5}{4}x - 15)
(y = -\frac{5}{4}x - 30)
(y = \frac{4}{5}x + 52)
(y = \frac{4}{5}x - 56)

Question

select the correct answer.

which equation represents the line that is perpendicular to (y = \frac{4}{5}x + 23) and passes through (-40,20)?

(y = -\frac{5}{4}x - 15)
(y = -\frac{5}{4}x - 30)
(y = \frac{4}{5}x + 52)
(y = \frac{4}{5}x - 56)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Slopes", "Negative Reciprocals", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Perpendicular Slopes", "Negative Reciprocals", "Slope-Intercept Form" ] } ## Find the perpendicular slope $$ \begin{aligned} &m_1 = \frac{4}{5} \ &m_2 = -\frac{1}{m_1} = -\frac{5}{4} \end{aligned} $$ ## Solve for the y-intercept $$ \begin{aligned} &y = m_2 x + b \ &20 = -\frac{5}{4}(-40) + b \ &20 = 50 + b \ &b = -30 \end{aligned} $$ ## Write the final equation $$ y = -\frac{5}{4}x - 30 $$

(A) $y = -\frac{4}{5}x - 15$

(B) $y = -\frac{5}{4}x - 30$

(C) $y = \frac{4}{5}x + 52$

(D) $y = \frac{4}{5}x - 56$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "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: