identify the lines which are parallel.

$y = 8x + 2$ and $y = 8x + 3$

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

Question

identify the lines which are parallel.

$y = 8x + 2$ and $y = 8x + 3$

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

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" ] } ## Identify the slopes of the first pair of lines $$ \begin{aligned} &y_1 = 8x + 2 \implies m_1 = 8 \ &y_2 = 8x + 3 \implies m_2 = 8 \end{aligned} $$ ## Identify the slopes of the second pair of lines $$ \begin{aligned} &y_3 = 3x - 2 \implies m_3 = 3 \ &y_4 = 4x + 2 \implies m_4 = 4 \end{aligned} $$ ## Compare slopes to determine parallel lines $$ \begin{aligned} &m_1 = m_2 = 8 \implies \text{Parallel} \ &m_3 e m_4 \implies \text{Not Parallel} \end{aligned} $$

(A) $y = 8x + 2$ and $y = 8x + 3$

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

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

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Question

Explanation:

Identify the slopes of the first pair of lines

Identify the slopes of the second pair of lines

Compare slopes to determine parallel lines

Answer: