Question

question 29 points 3

find the function which is parallel to \\(x + y = 9\\).

\\(2x + 2y = 2\\)

\\(x - y = 10\\)

Explanation:

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<reasoning>

Find the slope of the given line

\[

$$\begin{aligned} x + y &= 9 \\ y &= -x + 9 \end{aligned}$$

\]
The slope \(m_1\) is \(-1\).

Find the slopes of the options

For the first option:
\[

$$\begin{aligned} 2x + 2y &= 2 \\ 2y &= -2x + 2 \\ y &= -x + 1 \end{aligned}$$

\]
The slope \(m_2\) is \(-1\).

For the second option:
\[

$$\begin{aligned} x - y &= 10 \\ -y &= -x + 10 \\ y &= x - 10 \end{aligned}$$

\]
The slope \(m_3\) is \(1\).

Compare slopes for parallel lines

Parallel lines must have equal slopes:
\[
m_1 = m_2 = -1
\]
Thus, the line \(2x + 2y = 2\) is parallel to \(x + y = 9\).
</reasoning>

<answer>
<mcq-correct>(A) \(2x + 2y = 2\)</mcq-correct>
<mcq-option>(B) \(x - y = 10\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Find the slope of the given line

\[

$$\begin{aligned} x + y &= 9 \\ y &= -x + 9 \end{aligned}$$

\]
The slope \(m_1\) is \(-1\).

Find the slopes of the options

For the first option:
\[

$$\begin{aligned} 2x + 2y &= 2 \\ 2y &= -2x + 2 \\ y &= -x + 1 \end{aligned}$$

\]
The slope \(m_2\) is \(-1\).

For the second option:
\[

$$\begin{aligned} x - y &= 10 \\ -y &= -x + 10 \\ y &= x - 10 \end{aligned}$$

\]
The slope \(m_3\) is \(1\).

Compare slopes for parallel lines

Parallel lines must have equal slopes:
\[
m_1 = m_2 = -1
\]
Thus, the line \(2x + 2y = 2\) is parallel to \(x + y = 9\).
</reasoning>

<answer>
<mcq-correct>(A) \(2x + 2y = 2\)</mcq-correct>
<mcq-option>(B) \(x - y = 10\)</mcq-option>
</answer>

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"Parallel and Perpendicular Lines"
]
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