Answer
Option (d) is correct:
$y-2x=2$
$x+2y=-1$
Work Step by Step
Perpendicular lines have a negative inverse slope to the other (i.e. $\frac{a}{b}\rightarrow -\frac{b}{a}$), so let's rearrange the equations into the form y=mx+b to clearly see the value of their slopes. We get:
(a)
$y=2x+2$
$y=-2x-1$
(b)
$y=2x$
$y=-\frac{1}{2}x$
(c)
$y=\frac{1}{2}x+1$
$y=-\frac{1}{2}x-1$
(d)
$y=2x+2$
$y=-\frac{1}{2}x-\frac{1}{2}$
(e)
$y=-2x-2$
$y=-\frac{1}{2}x-1$
We can see that (a), (c), and (e)'s slopes aren't negatively inverse to each other, so they are out. We see in the graph that the lines don't intersect at the origin, leaving (b) out. That leaves us with (d), which is the correct answer.
