What the rule for the transformation is

What is the slope of the line shown below?

Leslie started last week with $1200 in her checking account. during the week, she wrote the checks below.

Let x have probability generating function gx (s) and let un generating function u(s) of the sequence uo, u1, satisfies p(x > n). show that the (1- s)u(s) = 1 - gx(s), whenever the series defining these generating functions converge.