Theresa, did you mean:
f(x) = -1/2 x + 7
(f(x+h) – f(x))/h is the Difference Quotient
f(x+h) = -1/2 (x+h) + 7
f(x+h) = -1/2 x – 1/2 h + 7
–f(x) = 1/2 x – 7
––––––––––––––––––––––
f(x+h) – f(x) = – 1/2 h
(f(x+h) – f(x))/h = – 1/2
[This is used in Calculus to "find the derivative of f(x)"]