what is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

$ y = -\frac{3}{4}x + 8 $
$ y = -\frac{3}{4}x + 6 $
$ y = \frac{4}{3}x - 8 $
$ y = \frac{4}{3}x - 6 $

Question

what is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

$ y = -\frac{3}{4}x + 8 $
$ y = -\frac{3}{4}x + 6 $
$ y = \frac{4}{3}x - 8 $
$ y = \frac{4}{3}x - 6 $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope Formula", "Perpendicular Slopes" ], "new_concepts": [ "Slope-Intercept Form" ], "current_concepts": [ "Slope Formula", "Perpendicular Slopes", "Slope-Intercept Form" ] } ## Find the slope of the given line $$ \begin{aligned} &(x_1, y_1) = (-4, 4)\ &(x_2, y_2) = (4, -2)\ &m_{\text{given}} = \frac{-2 - 4}{4 - (-4)} = \frac{-6}{8} = -\frac{3}{4} \end{aligned} $$ ## Determine the perpendicular slope $$ \begin{aligned} &m_{\perp} = -\frac{1}{m_{\text{given}}} = -\frac{1}{-\frac{3}{4}} = \frac{4}{3} \end{aligned} $$ ## Find the equation of the perpendicular line $$ \begin{aligned} &\text{Point: } (6, 0)\ &y - 0 = \frac{4}{3}(x - 6)\ &y = \frac{4}{3}x - 8 \end{aligned} $$

(A) $y = -\frac{3}{4}x + 8$

(B) $y = -\frac{3}{4}x + 6$

(C) $y = \frac{4}{3}x - 8$

(D) $y = \frac{4}{3}x - 6$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Slopes" ] }

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QUESTION IMAGE

Question

Explanation:

Find the slope of the given line

Determine the perpendicular slope

Find the equation of the perpendicular line

Answer: