###### 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

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

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 $$x\text{.}$$

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