Question

1. which line is parallel to the line given below?

$y = -\frac{4}{3}x + 1$
a. $3x + 4y = 8$
b. $3x - 4y = -28$
c. $4x + 3y = -15$
d. $4x - 3y = 9$

Explanation:

Step1: Recall Parallel Line Slope

Parallel lines have equal slopes. The given line is \( y = -\frac{4}{3}x + 1 \), so its slope (\( m \)) is \( -\frac{4}{3} \). We need to find the slope of each option by converting to slope - intercept form (\( y=mx + b \)).

Step2: Find Slope of Option A

For \( 3x + 4y=8 \), solve for \( y \):
\( 4y=-3x + 8 \)
\( y =-\frac{3}{4}x + 2 \). Slope is \( -\frac{3}{4}
eq-\frac{4}{3} \).

Step3: Find Slope of Option B

For \( 3x - 4y=-28 \), solve for \( y \):
\( - 4y=-3x - 28 \)
\( y=\frac{3}{4}x + 7 \). Slope is \( \frac{3}{4}
eq-\frac{4}{3} \).

Step4: Find Slope of Option C

For \( 4x + 3y=-15 \), solve for \( y \):
\( 3y=-4x - 15 \)
\( y =-\frac{4}{3}x-5 \). Slope is \( -\frac{4}{3} \), which matches the slope of the given line.

Step5: Find Slope of Option D

For \( 4x - 3y=9 \), solve for \( y \):
\( - 3y=-4x + 9 \)
\( y=\frac{4}{3}x - 3 \). Slope is \( \frac{4}{3}
eq-\frac{4}{3} \).

Answer:

C. \( 4x + 3y=-15 \)