which line is perpendicular to $5y + 2x = 5$?

$10x - 4y = 4$
$y + 5x = -2$
$2x + 5y = 10$
$y = -2x + 10$

choose the correct answer below.

a. $y = -2x + 10$
b. $y + 5x = -2$
c. $10x - 4y = 4$
d. $2x + 5y = 10$

Question

which line is perpendicular to $5y + 2x = 5$?

$10x - 4y = 4$
$y + 5x = -2$
$2x + 5y = 10$
$y = -2x + 10$

choose the correct answer below.

a. $y = -2x + 10$
b. $y + 5x = -2$
c. $10x - 4y = 4$
d. $2x + 5y = 10$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Perpendicular Lines", "Linear Equations" ] } ## Find the slope of the given line $$ \begin{aligned} 5y + 2x &= 5 \ 5y &= -2x + 5 \ y &= -\frac{2}{5}x + 1 \ m_1 &= -\frac{2}{5} \end{aligned} $$ ## Determine the perpendicular slope $$ \begin{aligned} m_2 &= -\frac{1}{m_1} \ m_2 &= -\frac{1}{-\frac{2}{5}} = \frac{5}{2} \end{aligned} $$ ## Identify the line with the perpendicular slope $$ \begin{aligned} 10x - 4y &= 4 \ -4y &= -10x + 4 \ y &= \frac{5}{2}x - 1 \ m &= \frac{5}{2} \end{aligned} $$

A. $y = -2x + 10$

B. $y + 5x = -2$

C. $10x - 4y = 4$

D. $2x + 5y = 10$

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

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QUESTION IMAGE

Question

Explanation:

Find the slope of the given line

Determine the perpendicular slope

Identify the line with the perpendicular slope

Answer: