write an equation of the line that is perpendicular to y=-x-6 and that passes through (9,-4)

Answer 1

Perpendicular Lines mean they have the negative reciprocal slope. This line has slope m = -1 so the perpendicular line has slope m = + 1.

Our point is (9, -4)

Now use point slope form to find the equation: (y - y₁) = m(x - x₁)

(y - y₁) = m(x - x₁)

(y - (-4)) = 1(x - 9)

y + 4 = x - 9

y = x - 13