Q.4 - Precalculus Enhanced with Graphing Utilities

Question

True or False Vertical lines have an undefined slope.

Step-by-Step Solution

Answer

The statement "Vertical lines have an undefined slope." is true.

Step 1. Given information.

We have:

Vertical lines have an undefined slope. 

Step 2. Find whether the statement is true or false.

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:

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

Hence, the statement "Vertical lines have an undefined slope."  is true.