Question

which equation represents a line which is parallel to the line $y = \frac{1}{2}x + 5$?

answer

$2y - x = 6$ $2x + y = 7$
$x + 2y = 8$ $2x - y = 2$

Explanation:

Step1: Recall parallel line slope rule

Parallel lines have equal slopes. The given line \( y = \frac{1}{2}x + 5 \) is in slope - intercept form \( y=mx + b \), where the slope \( m=\frac{1}{2} \). We need to find the slope of each option by rewriting them in slope - intercept form \( y = mx + b \).

Step2: Analyze option \( 2y - x=6 \)

Solve \( 2y - x = 6 \) for \( y \):
Add \( x \) to both sides: \( 2y=x + 6 \)
Divide both sides by 2: \( y=\frac{1}{2}x+3 \). The slope of this line is \( \frac{1}{2} \), which is equal to the slope of the given line. But let's check other options to be sure.

Step3: Analyze option \( 2x + y=7 \)

Solve \( 2x + y=7 \) for \( y \):
Subtract \( 2x \) from both sides: \( y=-2x + 7 \). The slope is \( - 2 \), which is not equal to \( \frac{1}{2} \).

Step4: Analyze option \( x + 2y=8 \)

Solve \( x + 2y=8 \) for \( y \):
Subtract \( x \) from both sides: \( 2y=-x + 8 \)
Divide by 2: \( y=-\frac{1}{2}x + 4 \). The slope is \( -\frac{1}{2} \), not equal to \( \frac{1}{2} \).

Step5: Analyze option \( 2x - y=2 \)

Solve \( 2x - y=2 \) for \( y \):
Subtract \( 2x \) from both sides: \( -y=-2x + 2 \)
Multiply both sides by - 1: \( y = 2x-2 \). The slope is \( 2 \), not equal to \( \frac{1}{2} \).

Answer:

A. \( 2y - x = 6 \)