Rewrite the equation into the general form: y=mx+b, where m represents slope.
We have:
x-y=8
-y=-x+8
y=x-8
Here, m happens to be 1. The slope of a perpendicular line to an equation is the negative reciprocal of the number.
For example, the negative reciprocal of 2 is -1/2 (so you 'flip' the number).
So the negative reciprocal of 1, or 1/1, is -1.
So the slope of the line perpendicular to that equation is -1.