Answer:
[tex]\frac{1}{2} x - 4[/tex]
Step-by-step explanation:
Perpendicular lines will have slopes that are the multiplicative additive inverse of each other: a line with slope 3/4 is perpendicular to a line with slope -4/3, for example. You need a line that is perpendicular to a line with slope -2 (reading that from the -2 in the -2x portion of the given equation, which is written in slope-intercept form), so your new line must have slope +1/2.
With the slope and a point, we can come up with an equation using this formula:
y - y-coordinate = slope (x - x-coordinate)
So we have y - (-2) = 1/2 (x - 4).
Simplify the equation: y + 2 = 1/2 x - 2
Subtract 2 from both sides: y + 2 - 2 = 1/2 x - 2 - 2
Simplify: y = 1/2 x - 4.
