###### Definition 4.3.12 Rate of Change

If \(\left(x_1,y_1\right)\) and \(\left(x_2,y_2\right)\) are two data points from a set of two-variable data, then the rate of change between them is

\begin{equation*}
\frac{\text{change in $y$}}{\text{change in $x$}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}\text{.}
\end{equation*}

(The Greek letter delta, \(\Delta\text{,}\) is used to represent “change in” since it is the first letter of the Greek word for “difference.”)