what is the equation of the line that is perpendicular to -x+y=7 and passes through (-1 , -1 )

Question

choices are

a)  -x+y=2

b)  -x-y=2

c)  x-y=2

d)  -x-y=0

e)  x+y=0

Answer 1

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).