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:

Identify the slope of the given line

Using the Slope of a Line and Point-Slope Form knowledge points

$$
LATEXBLOCK0
$$

Determine the slope of the parallel line

Using the Parallel Line Equations knowledge point

$$ m_{\text{parallel}} = m = 4 $$

Write the equation of the new line

Using the Point-Slope Form knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) \(y = -\frac{1}{4}x + 33\)
• (B) \(y = -\frac{1}{4}x + 36\)
• (C) \(y = 4x - 16\)
• (D) \(y = 4x + 16\) (Correct answer)