Here you see part of a graph of a function $y=f\left(x\right)$.

The mean change of this function $f$ on the interval $[a,b]$ is:
$\frac{(\Delta y)}{(\Delta x)}=\frac{(f\left(b\right)-f\left(a\right))}{(b-a)}$

This ratio of the difference between the values of the function at either end of the interval and the difference between the two values of $x$ is called the difference quotient of the function $f$ on the interval $[a,b]$.

In the graph of $f$ this difference quotient is equal to the slope of the line through $A(a,f(a\left)\right)$ and $B(b,f(b\left)\right)$.
This line is called a secant line $\mathrm{AB}$.