Question

what is the equation of the line that is parallel to the line (y - 1 = 4(x + 3)) and passes through the point ((4, 32))?

(y = -\frac{1}{4}x + 33)
(y = -\frac{1}{4}x + 36)
(y = 4x - 16)
(y = 4x + 16)

Explanation:

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<reasoning>

Determine the slope of the parallel line

\[

$$\begin{aligned} &y - 1 = 4(x + 3) \\ &m = 4 \end{aligned}$$

\]

Write the equation in point-slope form

\[

$$\begin{aligned} &(x_1, y_1) = (4, 32) \\ &y - 32 = 4(x - 4) \end{aligned}$$

\]

Convert to slope-intercept form

\[

$$\begin{aligned} &y - 32 = 4x - 16 \\ &y = 4x + 16 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(y = -\frac{1}{4}x + 33\)</mcq-option>
<mcq-option>(B) \(y = -\frac{1}{4}x + 36\)</mcq-option>
<mcq-option>(C) \(y = 4x - 16\)</mcq-option>
<mcq-correct>(D) \(y = 4x + 16\)</mcq-correct>
</answer>

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]
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Answer:

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<reasoning>

Determine the slope of the parallel line

\[

$$\begin{aligned} &y - 1 = 4(x + 3) \\ &m = 4 \end{aligned}$$

\]

Write the equation in point-slope form

\[

$$\begin{aligned} &(x_1, y_1) = (4, 32) \\ &y - 32 = 4(x - 4) \end{aligned}$$

\]

Convert to slope-intercept form

\[

$$\begin{aligned} &y - 32 = 4x - 16 \\ &y = 4x + 16 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(y = -\frac{1}{4}x + 33\)</mcq-option>
<mcq-option>(B) \(y = -\frac{1}{4}x + 36\)</mcq-option>
<mcq-option>(C) \(y = 4x - 16\)</mcq-option>
<mcq-correct>(D) \(y = 4x + 16\)</mcq-correct>
</answer>

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