Question

Write the equation of a line that is perpendicular to y = -X-6 and that passes through the point (-9, -4)

Answer 1

THe  line will have  slope -1/-1  = 1  so the general form is 

y - y1 = 1(x - x1)

x1 = -9 and y1 = -4 so:-

y + 4 = x  + 9

y = x + 5 is the equation you want

Answer 2

Given y = x-6 where the equation of a line is y = mx + c, i.e. if m = 1. then  1 x x = x. 

Now a line that is perpendicular to this perpendicular line must satisfy the formula:

m1.m2 = -1 

so, if the slope of our line is 1 (as I have shown) , then the opposite must be -1 , hence m = -1:

y = -1x + c