Question

1. which equation represents a line which is parallel to the line y = 1/2x + 3? a) y - 2x = -5 b) x - 2y = 2 c) 2x + y = -6 d) x + 2y = 4

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope. The given line $y=\frac{1}{2}x + 3$ has a slope $m=\frac{1}{2}$. Parallel lines have the same slope.

Step2: Rewrite each option in slope - intercept form

Option A

$y-2x=-5$ can be rewritten as $y = 2x-5$, slope $m = 2$.

Option B

$x - 2y=2$ can be rewritten as $-2y=-x + 2$, then $y=\frac{1}{2}x - 1$. The slope $m=\frac{1}{2}$.

Option C

$2x + y=-6$ can be rewritten as $y=-2x - 6$, slope $m=-2$.

Option D

$x + 2y=4$ can be rewritten as $2y=-x + 4$, then $y=-\frac{1}{2}x+2$, slope $m =-\frac{1}{2}$.

Answer:

B. $x - 2y = 2$