Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

The slope of a vertical line is ________ ; the slope of a horizontal line is _______.

Step-by-Step Solution

Answer

The slope of a vertical line is infinity; the slope of a horizontal line is zero.

Step 1. Given information.

The slope of a vertical line is ________ ; the slope of a horizontal line is _______.

Step 2. Find the slope of the vertical line.

The slope of the line is given by $m=\tan \theta$, where $\theta$ is the angle made by the given line with $x-$axis.

Now, a vertical line makes $90°$ angle with the $x-$ axis. Therefore, we get:

$$\begin{gathered} m=\tan 90 \\ m=\infty \end{gathered}$$

Step 3. Find slope of the horizontal line.

A horizontal line is a line parallel to the $x-$axis.

Therefore, we get:

$$\begin{gathered} m=\tan \theta \\ m=\tan 0 \\ m=0 \end{gathered}$$

Hence, the slope of a vertical line is infinity; the slope of a horizontal line is zero.