find the function which is perpendicular to (x + 2y = 6).

(2x - y = 5)
(x - y = 10)
(3x + 3y = 3)
all of the choices

Question

find the function which is perpendicular to (x + 2y = 6).

(2x - y = 5)
(x - y = 10)
(3x + 3y = 3)
all of the choices

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Slope of a Linear Function", "Parallel and Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Slope of a Linear Function", "Parallel and Perpendicular Lines", "Linear Equations" ] } ## Find the slope of the given line $$ \begin{aligned} x + 2y &= 6 \ 2y &= -x + 6 \ y &= -\frac{1}{2}x + 3 \ m_1 &= -\frac{1}{2} \end{aligned} $$ ## Determine the perpendicular slope $$ \begin{aligned} m_1 \cdot m_2 &= -1 \ -\frac{1}{2} \cdot m_2 &= -1 \ m_2 &= 2 \end{aligned} $$ ## Identify the matching option $$ \begin{aligned} 2x - y &= 5 \ y &= 2x - 5 \quad (\text{slope } m = 2) \end{aligned} $$

(A) $2x - y = 5$

(B) $x - y = 10$

(C) $3x + 3y = 3$

(D) All of the choices

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QUESTION IMAGE

Question

Explanation:

Find the slope of the given line

Determine the perpendicular slope

Identify the matching option

Answer: