question 16 points 2

choose the parallel lines from the following lines.

$y = 6x + 2$ and $3x - 2y = 4$

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

Question

question 16 points 2

choose the parallel lines from the following lines.

$y = 6x + 2$ and $3x - 2y = 4$

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

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 the slopes of the first pair of lines $$ \begin{aligned} &\text{Line 1: } y = 6x + 2 \implies m_1 = 6\ &\text{Line 2: } 3x - 2y = 4 \implies 2y = 3x - 4 \implies y = \frac{3}{2}x - 2 \implies m_2 = \frac{3}{2}\ &m_1 eq m_2 \end{aligned} $$ ## Find the slopes of the second pair of lines $$ \begin{aligned} &\text{Line 1: } y = 5x + 2 \implies m_1 = 5\ &\text{Line 2: } 5x - y = 2 \implies y = 5x - 2 \implies m_2 = 5\ &m_1 = m_2 = 5 \end{aligned} $$ ## Identify the parallel lines $$ \begin{aligned} &\text{Since the second pair of lines have equal slopes } (m = 5) \text{ and different } y\text{-intercepts } (2 eq -2)\text{, they are parallel.} \end{aligned} $$

(A) $y = 6x + 2$ and $3x - 2y = 4$

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

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "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

Identify the parallel lines

Answer: