Question

identify the lines which are parallel.

\\(y = 8x + 2\\) and \\(y = 8x + 3\\)

\\(y = 3x - 2\\) and \\(y = 4x + 2\\)

Explanation:

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<reasoning>

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

\[

$$\begin{aligned} &m_1 = m_2 = 8 \implies \text{Parallel} \\ &m_3 e m_4 \implies \text{Not Parallel} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(y = 8x + 2\) and \(y = 8x + 3\)</mcq-correct>
<mcq-option>(B) \(y = 3x - 2\) and \(y = 4x + 2\)</mcq-option>
</answer>

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"Mathematics",
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"Parallel and Perpendicular Lines"
]
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</post_analysis>

Answer:

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<reasoning>

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

\[

$$\begin{aligned} &m_1 = m_2 = 8 \implies \text{Parallel} \\ &m_3 e m_4 \implies \text{Not Parallel} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(y = 8x + 2\) and \(y = 8x + 3\)</mcq-correct>
<mcq-option>(B) \(y = 3x - 2\) and \(y = 4x + 2\)</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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]
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</post_analysis>