Answer:
y +2 = (1/2)(x -4)
Step-by-step explanation:
The given line's equation is in the slope-intercept form ...
y = mx + b
where m is the slope and b is the y-intercept. Matching your equation to this one, you see that m = -2. That is, the slope of the given line is -2.
The slope of the perpendicular line will be the opposite of the reciprocal of this slope, so will be ...
-1/(-2) = 1/2
__
We can use the desired slope and given point in the point-slope form of the equation of a line:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Filling in the values we want, m=1/2, (h, k) = (4, -2), gives us the equation ...
y +2 = (1/2)(x -4) . . . . the equation of your line
__
This can be rearranged to any of several other forms
y = 1/2x -4 . . . . . slope-intercept form
x -2y = 8 . . . . . . standard form
