What would be the perpendicular line for y equals -x-5?

Answer 1

If the gradient of a line is m, the gradient of a line perpendicular to it (m') is such that mm' = -1, that is:

m' = -1/m

So for:

y = -x - 5

m = -1, so the gradient of a perpendicular line is:

m' = -1/-1 = 1

So a general line perpendicular to y = -x - 5 would be:

y = x + c

A specific line perpendicular to y = -x - 5 at point (xo, -xo-5) on the line is:

y - (-xo-5) = 1(x - xo)

⇒ y = x - 2xo - 5