the equation of line lm is $5x - y = -4$. what is the equation of a line perpendicular to line lm in slope-intercept form that contains point $(-3, 2)$?

$y = 5x + 13$

$y = -\frac{1}{5}x +
\frac{7}{5}$

$y = -\frac{1}{5}x - \frac{7}{5}$

$y = 5x - 17$

Question

the equation of line lm is $5x - y = -4$. what is the equation of a line perpendicular to line lm in slope-intercept form that contains point $(-3, 2)$?

$y = 5x + 13$

$y = -\frac{1}{5}x +
\frac{7}{5}$

$y = -\frac{1}{5}x - \frac{7}{5}$

$y = 5x - 17$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Lines", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Perpendicular Lines", "Point-Slope Form", "Linear Functions" ] } ## Find the slope of line LM $$ \begin{aligned} 5x - y &= -4 \ y &= 5x + 4 \ m_1 &= 5 \end{aligned} $$ ## Determine the perpendicular slope $$ \begin{aligned} m_2 &= -\frac{1}{m_1} \ m_2 &= -\frac{1}{5} \end{aligned} $$ ## Write the equation in slope-intercept form using point (-3, 2) $$ \begin{aligned} y - y_1 &= m_2(x - x_1) \ y - 2 &= -\frac{1}{5}(x - (-3)) \ y - 2 &= -\frac{1}{5}(x + 3) \ y - 2 &= -\frac{1}{5}x - \frac{3}{5} \ y &= -\frac{1}{5}x - \frac{3}{5} + \frac{10}{5} \ y &= -\frac{1}{5}x + \frac{7}{5} \end{aligned} $$

(A) $y = 5x + 13$

(B) $y = -\frac{1}{5}x + \frac{7}{5}$

(C) $y = -\frac{1}{5}x - \frac{7}{5}$

(D) $y = 5x - 17$

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

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QUESTION IMAGE

Question

Explanation:

Find the slope of line LM

Determine the perpendicular slope

Write the equation in slope-intercept form using point (-3, 2)

Answer: