identify the parallel lines from the following.

$4x + 4y = 5$ and $y = 2x + 6$

$4x + 2y = 5$ and $y = -2x + 6$

Question

identify the parallel lines from the following.

$4x + 4y = 5$ and $y = 2x + 6$

$4x + 2y = 5$ and $y = -2x + 6$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope of a Linear Function", "Parallel and Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Slope of a Linear Function", "Parallel and Perpendicular Lines" ] } ## Find slopes of the first pair of lines $$ \begin{aligned} &4x + 4y = 5 \implies 4y = -4x + 5 \implies y = -x + \frac{5}{4} \implies m_1 = -1\ &y = 2x + 6 \implies m_2 = 2\ &m_1 eq m_2 \end{aligned} $$ ## Find slopes of the second pair of lines $$ \begin{aligned} &4x + 2y = 5 \implies 2y = -4x + 5 \implies y = -2x + \frac{5}{2} \implies m_1 = -2\ &y = -2x + 6 \implies m_2 = -2\ &m_1 = m_2 = -2 \end{aligned} $$

(A) $4x + 4y = 5$ and $y = 2x + 6$

(B) $4x + 2y = 5$ and $y = -2x + 6$

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

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QUESTION IMAGE

Question

Explanation:

Find slopes of the first pair of lines

Find slopes of the second pair of lines

Answer: