Egiven line passes through the points (−4, −3) and (4, 1). 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)

First find the slope of the two points 
The slope equation is m=y2-y1/x2-x1
m = 1 - (-3)/ 4 - (-4) = 4/8 = 1/2 

The point slope form is y-y1 = m(x-x1)
Choose any of the points, I'll choose (4,1) and plug it into the equation
y - 1 = 1/2 ( x-4 )

Now when you have a perpendicular line, its important to know the rules.
The first rule is that you have to find the reciprocal of the slope, 1/2 = 2/1 
So the slope is 2 
Now plug in the (-4,3) with the new slope found for the perpendicular line

y - 3 = 2(x+4)

Y - 3 = 2(x+4)
hope this helps!
have a good day:)