Chapter 1.1, Problem 65E

If, for some constant $m$,

$\frac{f(x_2)-f(x_1)}{x_2-x_1}=m$

for all $x_1\ne x_2$, show that $f\left(x\right)\text{=m}x\text{ + }b$, where $b$

is some constant. [Hint: Fix $x_1$

and take $x=x_2$; then, solve for $f(x)$.]