# What is Undefined Slope in Geometry?

Slope is an important concept in both algebra and geometry. It measures the steepness of a line and is used to help solve problems related to linear equations. When it comes to geometry, the slope of a line is determined by two points on the line, the rise and the run. The rise is the vertical distance between the two points, and the run is the horizontal distance between the two points. In this article, we'll discuss what it means when the slope of a line is undefined.

## What Does "Undefined" Mean?

In geometry, the term "undefined" means that the slope of a line cannot be determined. This often occurs when the line is either vertical or horizontal. A vertical line is a line that runs straight up and down and has no horizontal distance. A horizontal line is a line that runs straight across and has no vertical distance. In either of these cases, the rise and the run of the line will both be zero, and so the slope of the line cannot be calculated.

For example, take a look at the lines below. The first line is horizontal, and the second line is vertical. The run of the first line is zero, and the rise of the second line is zero. Therefore, the slopes of both of these lines are undefined.

## How Is Undefined Slope Used in Algebra?

In algebra, undefined slope is often used to solve linear equations. When an equation has two variables, such as x and y, the slope of the line that is formed by graphing the equation can be calculated using the formula m = (y2 - y1) / (x2 - x1). However, if the line that is formed by graphing the equation is either vertical or horizontal, the slope of the line will be undefined.

For example, take a look at the equation below. This equation can be graphed to form a horizontal line. Since the line is horizontal, the slope of the line is undefined. Therefore, the equation cannot be solved using the slope formula.

y = 7

## Practice Problems

Let's practice calculating the slope of lines and determining if the slope is undefined. In each of the problems below, draw the line on a coordinate plane and then calculate the slope of the line. If the slope of the line is undefined, write "undefined" as the answer.

- x = 3
- y = -4
- y = 4x + 2
- 3x - 2y = 6

Answers:

- undefined
- undefined
- m = 4
- m = -3/2

## Summary

In geometry, undefined slope means that the slope of a line cannot be determined. This often occurs when the line is either vertical or horizontal. In algebra, undefined slope is often used to solve linear equations. When an equation forms a vertical or horizontal line, the slope of the line will be undefined and the equation cannot be solved using the slope formula. Practice calculating the slope of lines to become more familiar with this concept.

## FAQ

### What is a undefined slope in geometry?

In geometry, an undefined slope, sometimes referred to as an "infinite slope," is a term used to describe a line that has no slope. This means that the line is either vertical or horizontal.

### What is an example of an undefined slope?

A vertical line is an example of an undefined slope. A vertical line is always straight up and down, so its slope is undefined since it does not have a rise over a run.

### How do you know if slope is undefined?

You can determine if a slope is undefined by looking at the line. If the line is either vertical or horizontal, then the slope is undefined.

### How do you write undefined slope?

Undefined slope is typically written as either "no slope" or "infinite slope."