###### Definition4.4.3Slope

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 \(x\text{.}\)