Question

find the function which is perpendicular to \\(2y = -8x + 2\\).

\\(y = -4x + 8\\)
\\(y = 1/4x + 8\\)
\\(y = -1/4x + 8\\)
all of the choices

Explanation:

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<reasoning>

Find slope of given line

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} 2y &= -8x + 2 \\ y &= -4x + 1 \end{aligned}$$

\]
The slope \(m_1\) is \(-4\).

Determine perpendicular slope

Using the Parallel and Perpendicular Lines knowledge point
\[

$$\begin{aligned} m_2 &= -\frac{1}{m_1} \\ m_2 &= -\frac{1}{-4} = \frac{1}{4} \end{aligned}$$

\]

Identify matching function

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} y &= \frac{1}{4}x + 8 \end{aligned}$$

\]
This equation has the required slope of \(\frac{1}{4}\).
</reasoning>

<answer>
<mcq-option>(A) \(y = -4x + 8\)</mcq-option>
<mcq-correct>(B) \(y = 1/4x + 8\)</mcq-correct>
<mcq-option>(C) \(y = -1/4x + 8\)</mcq-option>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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Answer:

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<reasoning>

Find slope of given line

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} 2y &= -8x + 2 \\ y &= -4x + 1 \end{aligned}$$

\]
The slope \(m_1\) is \(-4\).

Determine perpendicular slope

Using the Parallel and Perpendicular Lines knowledge point
\[

$$\begin{aligned} m_2 &= -\frac{1}{m_1} \\ m_2 &= -\frac{1}{-4} = \frac{1}{4} \end{aligned}$$

\]

Identify matching function

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} y &= \frac{1}{4}x + 8 \end{aligned}$$

\]
This equation has the required slope of \(\frac{1}{4}\).
</reasoning>

<answer>
<mcq-option>(A) \(y = -4x + 8\)</mcq-option>
<mcq-correct>(B) \(y = 1/4x + 8\)</mcq-correct>
<mcq-option>(C) \(y = -1/4x + 8\)</mcq-option>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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