Question

which equation represents a line which is parallel to the line $y = \frac{3}{8}x + 7$?

answer

$8x + 3y = -12$ $8x - 3y = 18$
$8y - 3x = 32$ $3x + 8y = 8$

Explanation:

Step1: Recall parallel line slope rule

Parallel lines have equal slopes. The given line \( y = \frac{3}{8}x + 7 \) is in slope - intercept form \( y=mx + b \), where the slope \( m=\frac{3}{8} \). We need to find the slope of each option by converting them to slope - intercept form \( y = mx + b \).

Step2: Analyze Option 1: \( 8x + 3y=-12 \)

Solve for \( y \):
\( 3y=-8x - 12 \)
\( y=-\frac{8}{3}x-4 \)
The slope \( m =-\frac{8}{3}\), not equal to \( \frac{3}{8} \).

Step3: Analyze Option 2: \( 8x - 3y = 18 \)

Solve for \( y \):
\( - 3y=-8x + 18 \)
\( y=\frac{8}{3}x - 6 \)
The slope \( m=\frac{8}{3}\), not equal to \( \frac{3}{8} \).

Step4: Analyze Option 3: \( 8y-3x = 32 \)

Solve for \( y \):
\( 8y=3x + 32 \)
\( y=\frac{3}{8}x + 4 \)
The slope \( m = \frac{3}{8}\), which is equal to the slope of the given line.

Step5: Analyze Option 4: \( 3x + 8y=8 \)

Solve for \( y \):
\( 8y=-3x + 8 \)
\( y=-\frac{3}{8}x + 1 \)
The slope \( m=-\frac{3}{8}\), not equal to \( \frac{3}{8} \).

Answer:

\( 8y - 3x = 32 \) (the third option)