[tex]y+8 = \frac{1}{2}(x-7)[/tex] is equivalent to [tex]y-(-8) = \frac{1}{2}(x-7)[/tex]
That is in the form [tex]y-y_{1} = m(x-x_{1})[/tex] which is point slope form
In this case,
m = 1/2 is the slope
(x1,y1) = (7,-8) is the point the line goes through