First find f(x+h) by substituting (x+h) for x



Then substitute in the expression at the top:



Now simplify. Remove the inner parentheses:



Remove the other parentheses:









   <-- answer

Notice that the slope of f(x) = ax+b is a [Thinking of y=mx+b]

This demonstrates that the difference quotient of a linear function
is always equal to the slope of the line. [I just threw that in.]

Edwin