f(x) = 3x + 9
f(x+h) = 3(x+h) + 9 = 3x + 3h + 9
f(x+h) - f(x) = (3x + 3h + 9) - (3x + 9) = 3h
[f(x+h)-f(x)] / h = 3h/h = 3 (as long as h≠0)
The difference quotient is a variation of the slope formula. For linear functions, the difference quotient will always work out to be the slope of the line. For non-linear functions, the difference quotient will be a formula.