Find the slope of a line perpendiculat to the line y=1/2x+7

Answer 1

Pretty easy. Use the fact that the product of the first derivatives of linear functions and their perpendiculars respectively are always -1.
This is:
m'=-1/(1/2)=-2
Since we can choose an arbitrary function with the imposed properties, it suffices to take
g(x)=-2*x
q.e.d.