Horizontal and vertical lines have specific characteristics, and they have unique slope values. The example boxes below compare horizontal and vertical lines.
A line on the coordinate plane. The line is perfectly flat as you read it from left to right. The following points on the line are labelled with their ordered pairs:
Does not rise or fall as you read it from left to right.
All of the ordered pairs that lie along a horizontal line have identical \( y \)-coordinates.
The slope value is 0.
A line on the coordinate plane. The line is runs up and down. The following points on the line are labelled with their ordered pairs:
Runs up and down in the coordinate plane.
All of the ordered pairs that lie along a vertical line have identical \( x \)-coordinates.
The slope is undefined.
Remember that a horizontal line has a slope value of 0 because it has no steepness. In the slope formula, \( m = \frac{\text{rise}}{\text{run}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \), all horizontal lines have a rise value of 0.
A vertical line has an undefined slope because in the slope formula, \( m = \frac{\text{rise}}{\text{run}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \), it has a run value of 0. This is true for all vertical lines.
Use what you have learned about horizontal and vertical lines to complete the activity below. Calculate the slope value of the line that is described on each slide, then check your answer.
