Hello,

I have to show that for some constant m:

$\displaystyle \frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}=m$

For all $\displaystyle x_{1}$≠$\displaystyle x_{2}$, show that f(x)=mx+b, where b is some constant. The hint given is to fix $\displaystyle x_{1}$ and take x=x$\displaystyle x_{2}$; then solve for f(x).

I figured that I should change it to point slope form like this (referring to the hint given):

But I'm not sure if this step is correct or not and how I can turn it into the slope-intercept form? Please help.