Answer
The answer is
$$k=\frac{f(a)-f(b)}{a-b}.$$
Work Step by Step
The equation of the line is of the form of
$$y=kx+n$$
where $k$ and $n$ are constants and $k$ is called the slope of the line.
Since this line passes through the points $(a,f(a))$ and $(b,f(b))$ it must be:
$$f(a)=ka+n;\quad f(b)=kb+n.$$
Subtracting those equations we get
$$f(a)-f(b)=k(a-b)$$ so the slope s equal to
$$k=\frac{f(a)-f(b)}{a-b}.$$
