find the equation of the line that passes through the point (-5, 5) and is perpendicular to (y = \frac{5}{9}x - 4)

$y = -\frac{9}{5}x - 2$
$y = \frac{5}{9}x + 1$
$y = -\frac{9}{5}x - 4$
$y = 5x - 8$

Question

find the equation of the line that passes through the point (-5, 5) and is perpendicular to (y = \frac{5}{9}x - 4)

$y = -\frac{9}{5}x - 2$
$y = \frac{5}{9}x + 1$
$y = -\frac{9}{5}x - 4$
$y = 5x - 8$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Perpendicular Lines Slopes", "Point-Slope Form", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Perpendicular Lines Slopes", "Point-Slope Form", "Slope-Intercept Form" ] } ## Find the slope of the perpendicular line Using the *Perpendicular Lines Slopes* knowledge point $$ \begin{aligned} &m_1 = \frac{5}{9}\ &m_2 = -\frac{1}{m_1} = -\frac{9}{5} \end{aligned} $$ ## Write the equation in point-slope form Using the *Point-Slope Form* knowledge point $$ \begin{aligned} &(x_1, y_1) = (-5, 5)\ &y - 5 = -\frac{9}{5}(x - (-5))\ &y - 5 = -\frac{9}{5}(x + 5) \end{aligned} $$ ## Convert to slope-intercept form Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y - 5 = -\frac{9}{5}x - 9\ &y = -\frac{9}{5}x - 4 \end{aligned} $$

(A) $y = -\frac{9}{5}x - 2$

(B) $y = \frac{5}{9}x + 1$

(C) $y = -\frac{9}{5}x - 4$

(D) $y = 5x - 8$

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QUESTION IMAGE

Question

Explanation:

Find the slope of the perpendicular line

Write the equation in point-slope form

Convert to slope-intercept form

Answer: