Question

1. which of the following lines are parallel to $y = \frac{1}{2}x - 5$?

a. $y = \frac{1}{4}x + 5$
b. $y = -\frac{1}{2}x + 2$
c. $y = 4 + \frac{4}{8}x$

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( Y = \frac{1}{2}X - 5 \), so its slope \( m = \frac{1}{2} \).

Step2: Find slope of each option

• Option A: \( Y = \frac{1}{4}X + 5 \), slope \( m_A = \frac{1}{4}

eq \frac{1}{2} \).

• Option B: \( Y = -\frac{1}{2}X + 2 \), slope \( m_B = -\frac{1}{2}

eq \frac{1}{2} \).

• Option C: Simplify \( \frac{4}{8} = \frac{1}{2} \), so \( Y = 4 + \frac{1}{2}X \), slope \( m_C = \frac{1}{2} \), which equals the slope of the given line.

Answer:

C. \( Y = 4 + \frac{4}{8}X \)