Chapter 3.3, Problem 48HP

To determine

To explain why the slope formula does not work for vertical lines.

Explanation of Solution

Given:

Why does the slope formula not work for vertical lines?

Concept Used:

Equation of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $y-y_1=m\left(x-x_1\right)$ , where $\text{slope, }m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

The slope of any line is given by rise over run. That is, the ratio of the number of units it rise or fall over the number of units it move forward or backward from a fixed point.

A vertical line is a line parallel to the y -axis or the vertical axis. And for any vertical line, at any point of the line, the x -coordinate remains same for all points.

In the slope formula, the denominator gives the difference of x -coordinates of any two points. But for the vertical lines, the x -coordinate of all points is same, so the difference will become 0. That is, the denominator will become 0 in the slope formula, which will result in an undefined expression. Because anything divided by 0 is not defined.

That’s why the slope formula does not work for the vertical lines.