point slope form is
where the slope of the line is m and a point on the line is

first find slope
the slope between (10,5) and (4,-7) is (-7-5)/(4-10)=-12/-6=2
the slope is 2, m=2
we can use the point (10,5) or (4,-7)
remember, (x,y)
so our possible equations are
and

answer is C