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# The Slope of a Line Study Guide

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Updated on Oct 5, 2011

## Introduction to The Slope of a Line

### Lesson Summary

In this lesson, you will learn how to determine the slope of a line from its graph or from two points on the line. You will also learn how to tell by sight if the slope of a line is positive, negative, zero, or undefined.

The slope of a line is the measure of its steepness. The slope of a line is determined by the ratio of its rise to run. When looking at a line on a coordinate grid, always count the run before you count the rise. When a line points up to the right, it has a positive slope. A line with a negative slope points up to the left.

#### Examples:

Find the slope of each line.

## Special Cases of Slope

You may be wondering what the slope is for horizontal and vertical lines—these two types of lines do not slant up toward the left or the right. They are special cases.

The horizontal line has a slope of zero, since the rise is equal to zero. (Remember that zero divided by anything equals zero, so ) On the other hand, the vertical line has an undefined slope (sometimes said to have "no slope"). In this case, the run is equal to zero, so and a number divided by zero is said to be undefined, since it doesn't make sense to take something and divide it up into zero parts. The following illustrations may help you remember which type of line—horizontal or vertical—has an undefined (no slope) or a slope of zero.

## Using Slope Formula

You can also use a formula to determine the slope of a line containing two points, point A(x1,y1) and point B(x2,y2). Here is the formula:

#### Example:

Find the slope of the line through P(–6,5) and Q(–2,–1).

#### Solution:

Begin by labeling the coordinates before you insert the values into the formula.

Practice problems for these concepts can be found at: The Slope of a Line Practice Questions.

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