Question

a given line has the equation \\(10x+2y=-2\\).

what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point \\((0, 12)\\)?

\\(\bigcirc\\) \\(y=-5x+12\\)
\\(\bigcirc\\) \\(5x+y=12\\)
\\(\bigcirc\\) \\(y-12=5(x-0)\\)
\\(\bigcirc\\) \\(5x+y=-1\\)

Explanation:

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<reasoning>

Find the slope of the given line

\[

$$\begin{aligned} 10x + 2y &= -2 \\ 2y &= -10x - 2 \\ y &= -5x - 1 \end{aligned}$$

\]
\[
m = -5
\]

Determine the equation of the parallel line

\[

$$\begin{aligned} m_{\text{parallel}} &= -5 \\ (x_1, y_1) &= (0, 12) \\ y - 12 &= -5(x - 0) \\ y &= -5x + 12 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(y=-5x+12\)</mcq-correct>
<mcq-option>(B) \(5x+y=12\)</mcq-option>
<mcq-option>(C) \(y-12=5(x-0)\)</mcq-option>
<mcq-option>(D) \(5x+y=-1\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Find the slope of the given line

\[

$$\begin{aligned} 10x + 2y &= -2 \\ 2y &= -10x - 2 \\ y &= -5x - 1 \end{aligned}$$

\]
\[
m = -5
\]

Determine the equation of the parallel line

\[

$$\begin{aligned} m_{\text{parallel}} &= -5 \\ (x_1, y_1) &= (0, 12) \\ y - 12 &= -5(x - 0) \\ y &= -5x + 12 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(y=-5x+12\)</mcq-correct>
<mcq-option>(B) \(5x+y=12\)</mcq-option>
<mcq-option>(C) \(y-12=5(x-0)\)</mcq-option>
<mcq-option>(D) \(5x+y=-1\)</mcq-option>
</answer>

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