###### Example4.8.10Zero Slope

In Checkpoint 4.4.22, we learned that a horizontal line's slope is $$0\text{,}$$ because the distance doesn't change as time moves on. So the numerator in the slope formula (4.4.3) is $$0\text{.}$$ Now, if we know a line's slope and its $$y$$-intercept, we can use slope-intercept form (4.5.1) to write its equation:

\begin{align*} y\amp=mx+b\\ y\amp=0x+b\\ y\amp=b \end{align*}

This provides us with an alternative way to think about equations of horizontal lines. They have a certain $$y$$-intercept $$b\text{,}$$ and they have slope $$0\text{.}$$

We use horizontal lines to model scenarios where there is no change in $$y$$-values, like when Tammy stopped for $$12$$ hours (she deserved a rest!)

in-context