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)

You can read off the changes in x and y directly from the given graph.  The change in y is positive and is 4-(-3), or 7, and the change in x is positive and is 4-(-4), or 8.  Thus, the slope is m = 7/8.

In point-slope form:

y-3 = (7/8)(x-[-4]), or   y-3 = (7/8)(x+4)      (answer in point-slope form)