# Undefined Slope: Definition & Examples - Video & Lesson Transcript

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

## What Is an Undefined Slope?

The slope of a line is undefined if the line is vertical. If you think of slope as rise over run, then the line rises an infinite amount, or goes straight up, but does not run at all

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0:05 What Is an Undefined Slope? (Source: study.com)

0:05 What Is an Undefined Slope? (Source: study.com)

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## Undefined Slop

In the xy-coordinate plane, the slope of a line is a way of measuring its “steepness”. A large positive slope, for example, means that the line rises from left to right very quickly. But considering this, how can we have an undefined slope? The answer is based on how we calculate slope with the slope formula. In this lesson, we will look at what kinds of lines have an undefined slope and at why this is the case. (Source: www.mathbootcamps.com)

## What Kinds of Lines Have an Undefined Slope?

Any vertical line, like the one shown below, will have an undefined slope. These lines are always of the form \(x = c\), where \(c\) is some number. (Source: www.mathbootcamps.com)

## Why Is the Slope Undefined for Vertical Lines?

Let’s use the example of the line \(x = 4\), which is graphed above. Two points on this line would be \((4, 1)\) and \((4, 2)\). Since you can use any two points to calculate the slope of the line, we can then apply the slope formula using \((x_1,y_1) = (4,1)\) and \((x_2, y_2) = (4,2)\). (Source: www.mathbootcamps.com)

## Biomath: Linear Functions

where m is the slope of the line, and b is the y-intercept. We call b the y-intercept because the graph of y = mx + b intersects the y-axis at the point (0, b). We can verify this by substituting x = 0 into the equation as, (Source: www.biology.arizona.edu)

## Types of Slopes of a Lin

Generally, there are three (3) types of slopes of a line, namely positive, negative, and zero slopes. The fourth one is a bit controversial. (Source: www.chilimath.com)