What is the equation of a line that is perpendicular to 2x + y = −4 and passes through the point (2,−8)? the answer should be in the form y = mx +b. much appreciated.

Perpendicular is a 90 degree angle which means that it could just be the opposite of one of the numbers and it be just fine so I believe your answer would be  2x + y = 4 but I may be wrong

2x + y = -4

First rearrange this in to the form (y = mx + c).

y = -2x - 4

When a line is perpendicular to another line, its gradient must be inverted, and we do this by (-1 / m). In this case our gradient is -2, so the gradient for the new line is (1/2).

To find our constant (c) for this new equation, we can use (y - y1) = m(x - x1).

We replace y1 with -8, and x1 with 2, as we know the new line passes through this point. And we also replace m, our gradient, with the gradient we found earlier, (1/2).

y -- 8 = (1/2)(x - 2)

y + 8 = (1/2)x - 1

Now we just rearrange in to the form (y = mx + c)

y = (1/2)x - 9