is this parallel, perpendicular, or neither??

y+x = -2 and y-x= -2

First transform the equation to a form easy to calculate the slope, m.

y=-x-2 and
y=x-2
So the slopes are -1 and 1 respectively.
The two lines are perpendicular to each other when the product of the slope is -1.
Can you take it from here?