What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4,3)? the given line passes through the points (-4,-3) and (4,1)

The slope of the given line is
.. (1 -(-3))/(4 -(-4)) = 4/8 = 1/2
Then the perpendicular line will have slope
.. m = -1/(1/2) = -2

The point-slope form of your line is
.. y -3 = -2(x +4) . . . . . . . . . . if you prefer y -y0 = m(x -x0)
.. y = -2(x +4) +3 . . . . . . . . . . if you prefer y = m(x -x0) +y0 as I do.