Chapter 8.4, Problem 34E

To determine

To describe:

The difference between a line with zero slope and a line with undefined slope.

Answer to Problem 34E

A line with zero slope has zero rise, while a line with undefined slope has zero run.

Explanation of Solution

We know that the slope of a line is equal to rise over run, or vertical change over horizontal change.

We can find rise of a line by finding the difference of two y -coordinates, while we can find run by taking difference between the x -coordinates.

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1},\text{where,}\\ m=\text{Slope of line,}\\ y_2-y_1=\text{Difference between two }y\text{-coordinates}\\ x_2-x_1=\text{Difference between two }x\text{-coordinates of same }y-\text{coordinates}\end{array}$

We know that slope of a vertical line is undefined as the difference between two x -coordinates on a vertical line is 0. That results in a division by 0.

We also know that slope of a horizontal line is zeroas the difference between two y- coordinates on a vertical line is 0.

A line with zero slope has zero rise, while a line with undefined slope has zero run.