identify the perpendicular lines from the following.

$4y = 2 + 4x$ and $2y = 5 + 2x$

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

Question

identify the perpendicular lines from the following.

$4y = 2 + 4x$ and $2y = 5 + 2x$

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallel and Perpendicular Lines", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Parallel and Perpendicular Lines", "Slope-Intercept Form", "Slope of a Linear Function" ] } ## Find the slopes of the first pair of lines $$ \begin{aligned} 4y &= 2 + 4x \implies y = x + \frac{1}{2} \implies m_1 = 1\ 2y &= 5 + 2x \implies y = x + \frac{5}{2} \implies m_2 = 1 \end{aligned} $$ ## Find the slopes of the second pair of lines $$ \begin{aligned} 4y &= 2 + 4x \implies y = x + \frac{1}{2} \implies m_1 = 1\ 2y &= 5 - 2x \implies y = -x + \frac{5}{2} \implies m_2 = -1 \end{aligned} $$ ## Check the perpendicular condition $$ m_1 \cdot m_2 = 1 \cdot (-1) = -1 $$

(A) $4y = 2 + 4x$ and $2y = 5 + 2x$

(B) $4y = 2 + 4x$ and $2y = 5 - 2x$

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

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QUESTION IMAGE

Question

Explanation:

Find the slopes of the first pair of lines

Find the slopes of the second pair of lines

Check the perpendicular condition

Answer: