Vertical line

Definition

A vertical line is a straight line that goes up and down and has an undefined slope. It is represented by the equation $x = a$ where $a$ is a constant.

5 Must Know Facts For Your Next Test

1. A vertical line has an undefined slope because the change in x-coordinates is zero, resulting in division by zero.
2. The equation of a vertical line is always in the form $x = a$, where $a$ is a specific value on the x-axis.
3. A vertical line does not intersect the y-axis unless at infinity, meaning it only intersects points where x equals the constant value.
4. In coordinate geometry, vertical lines are perpendicular to horizontal lines which have equations of the form $y = b$.
5. The graph of a linear function cannot be a vertical line since linear functions require each input to map to exactly one output.

Review Questions

• What is the general form of the equation for any vertical line?
• Why does a vertical line have an undefined slope?
• How does a vertical line differ from the graph of a linear function?

Related terms

Slope:

The measure of steepness or incline of a line, calculated as the ratio of rise over run between two points on the line.

Linear Equation:

An equation that makes a straight line when graphed. It typically has the form $y = mx + b$.

Horizontal Line: A straight line that runs left to right and has zero slope. Its equation is in the form $y = b$, where $b$ is a constant.