Question

1. which line is parallel to the line with the equation $y = \frac{3}{4}x + 12$.

a. $y = \frac{3}{4}x - 7$
b. $y = -\frac{4}{3}x + 4$
c. $y = \frac{4}{3}x + 2$
d. $y = -\frac{3}{4}x + 5$

Explanation:

Step1: Recall Parallel Line Slopes

Parallel lines have equal slopes. The given line is \( y = \frac{3}{4}x + 12 \), so its slope (\( m \)) is \( \frac{3}{4} \).

Step2: Check Each Option's Slope

• Option A: \( y = \frac{3}{4}x - 7 \) has slope \( \frac{3}{4} \), same as given line.
• Option B: \( y = -\frac{4}{3}x + 4 \) has slope \( -\frac{4}{3} \), not equal.
• Option C: \( y = \frac{4}{3}x + 2 \) has slope \( \frac{4}{3} \), not equal.
• Option D: \( y = -\frac{3}{4}x + 5 \) has slope \( -\frac{3}{4} \), not equal.

Answer:

A. \( y = \frac{3}{4}x - 7 \)