Get the equation into standard form: y=x+7. This tells us the slope is 1.
The perpendicular has the negative of this slope, i.e., -1, so the equation of the perpendicular is y=-x+b, where b is a value we must find by substituting the (x,y) corresponding to (-1,-1):
-1=+1+b, from which b=-2, so y=-x-2.
Rearranging this we get -x-y=2, which is answer b).