Chapter 3.3, Problem 48HP

To determine

To Explain:the slope formula not work for vertical lines.

Explanation of Solution

The slope formulae joining two points $(x_1,y_1)\text{ and }(x_2,y_2)$ is given by,

  $m=\frac{y_2-y_1}{x_2-x_1}$ , Where m is slope of any line.

For a vertical line the x-coordinates are always equal and hence $x_1=x_2$

  $\Rightarrow x_2-x_1=0$

If we put this value in slope formulae we will get

  $m=\frac{y_2-y_1}{0}=\infty$

Here m is undefined and slope of vertical line is always undefined.

This is true for all vertical lines.

That’s why slope formuladoes not work for vertical lines.