Question

identify the parallel lines from the following.

\\(4x + 4y = 5\\) and \\(y = 2x + 6\\)

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

Explanation:

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<reasoning>

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

\[

$$\begin{aligned} &4x + 2y = 5 \implies 2y = -4x + 5 \implies y = -2x + \frac{5}{2} \implies m_1 = -2\\ &y = -2x + 6 \implies m_2 = -2\\ &m_1 = m_2 = -2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(4x + 4y = 5\) and \(y = 2x + 6\)</mcq-option>
<mcq-correct>(B) \(4x + 2y = 5\) and \(y = -2x + 6\)</mcq-correct>
</answer>

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]
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Answer:

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<reasoning>

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

\[

$$\begin{aligned} &4x + 2y = 5 \implies 2y = -4x + 5 \implies y = -2x + \frac{5}{2} \implies m_1 = -2\\ &y = -2x + 6 \implies m_2 = -2\\ &m_1 = m_2 = -2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(4x + 4y = 5\) and \(y = 2x + 6\)</mcq-option>
<mcq-correct>(B) \(4x + 2y = 5\) and \(y = -2x + 6\)</mcq-correct>
</answer>

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