When \(x\) and \(y\) are two variables where the rate of change between any two points is always the same, we call this common rate of change the slope. Since having a constant rate of change means the graph will be a straight line, it's also called the slope of the line.

Considering the definition for Definition 4.3.12, this means that you can calculate slope, \(m\text{,}\) as

\begin{equation} m=\frac{\text{change in $y$}}{\text{change in $x$}}=\frac{\Delta y}{\Delta x}\tag{4.4.1} \end{equation}

when \(x\) and \(y\) have a linear relationship.

A slope is a rate of change. So if there are units for the horizontal and vertical variables, then there will be units for the slope. The slope will be measured in \(\frac{\text{vertical units}}{\text{horizontal units}}\text{.}\)

If the slope is nonzero, we say that there is a linear relationship between \(x\) and \(y\text{.}\) When the slope is \(0\text{,}\) we say that \(y\) is constant with respect to \(x\text{.}\)