An equation in point-slope form that passes through point P(a,b) is as follows:
y-b=m(x-a) where m=slope, a,b are coordinates of point P.
For a line to pass through P(4,-8) the equation will look like: y-(-8) = m(x-4) simplify left side y+8=m(x-4)
The given equation has a slope of m=-1/2, so the slope of a line perpendicular to it has a slope of -1/m = -1/(-1/2)=+2
Now go through the answer choices: a. y+8=2(x-4) => passes through P(4,-8) and has a slope of 2. so TRUE b. y-4=2(x+8) => has a slope of 2, but passes through (-8,4), which is not P so FALSE c. y+8=(1/2)(x-4) => passes through P(4,-8), but has the wrong slope (a reflection, not perpendicular) so FALSE d. y-8=(1/2)(x+4) => passes through a wrong point (-4,8) and has the reflected slope (not perpendicular) so FALSE
