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!)