Chapter 1.3, Problem 104E

To determine

To explain: why the slope of a vertical line is undefined.

Explanation of Solution

Concept Used:

Slope of a line:

The slope of line passing through two point $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$ .

A vertical line is a line whose x -coordinate does not changes no matter what its y - coordinate is.

That is any two different points on this line will be of form $\left(x,y_1\right)$ and $\left(x,y_2\right)$ .

Now, by the above formula, slope of this line will be,

  $\begin{array}{c}m=\frac{y_2-y_1}{x-x}\\ =\frac{y_2-y_1}{0}\end{array}$

But division by zero is not defined.

Hence, the slope of a vertical line is undefined.