It it's perpendicular to y= -2x-8, then you take the opposite reciprocal of -2 which is (1/2).
[tex]y - ( - 2) = \frac{1}{2}(x - 4) \\ y + 2 = \frac{1}{2} x - \frac{4}{2} \\ y + 2 = \frac{1}{2}x - 2 \\ y = \frac{1}{2}x - 4[/tex]
The equation is
[tex]y = \frac{1}{2}x - 4[/tex]
