Chapter 8.3, Problem 23WE

To determine

To calculate: The slope of the line,

  $x=2$

Answer to Problem 23WE

Theslope of the lineundefined that means the line has no slope.

Explanation of Solution

Given information:

Theequation of the lines:

  $x=2$

Formula used:

For finding the slope of the line:

  $m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Consider the equation of line,

  $x=2$

The general equation of line is:

  $ax+b=y$

Here in this form this equation becomes:

  $\begin{array}{l}ax+b=y\\ x-4=y\end{array}$

For finding the slope of line when apply values in the formula,

  $m=\frac{y_2-y_1}{x_2-x_1}$

The points :

For $\left(2,2\right),\left(2,-3\right)$ , find the slope:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-3-2}{2-2}\\ m=-5\end{array}$

Observe that, the result will found here is negative value and as we know the slope of negative value is undefined.

So the slope of the equation $x=2$ is undefined.

Line $x=2$ has no slope.

The graph of the line is vertical line through $x=2$ .

A line that no rises , the slope of that line is undefined.

Thus, the slope of the line is undefined that means a line $x=2$ has no slope.