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# The Equation of a Line Study Guide

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Updated on Oct 5, 2011

## Introduction to The Equation of a Line

### Lesson Summary

In this lesson, you will learn how to identify linear equations. You will also learn how to use the equation of a line to find points on the line. You will also determine if an ordered pair is on a line using the equation of the line.

People often make comparisons among numbers. For example, a nurse looks at a patient's temperature over a period of time. A salesperson will compare commissions from sports cars and family vans. These types of comparisons can often be graphed in a straight line to make predictions about future events. This straight line may be created by using a linear equation.

## What Is a Linear Equation?

The standard form for a linear equation is Ax + By = C, where A, B, and C are constants; A and B cannot both be equal to zero. Linear equations will not have exponents on the variables x and y. The product or quotient of variables is not found in linear equations. Take a look at the following examples of linear and nonlinear equations.

## Points on a Line

When you graph multiple points on a coordinate plane, you can easily see whether they could be connected to form a straight line. However, it is possible for you to determine whether a point is on a line or satisfies the equation of a line without using a coordinate plane. If the ordered pair can replace x and y, and the result is a true statement, then the ordered pair is a point on the line.

#### Examples:

Determine if the ordered pairs satisfy the linear equation 2xy = 4.

1.     (2,2)     Solution: 2xy = 4
2.                                 2(2) – 2 4

4 – 2 4

2 ≠ 4

no; (2,2) is not on the line 2xy = 4.

3.     (0,–4)     Solution: 2xy = 4
4.                                   2(0) – (–4) 4

0 + 4 4

4 = 4

yes; (0,–4) is on the line 2xy = 4.

## Graphing Linear Equations

You can graph any linear equation you want by choosing several x or y coordinates to substitute into the original equation, and then solve the equation to find the other variable. This is easier if you organize your work into a table. You could choose any values you want and get a solution that would be an ordered pair or point on the line, but for this example, let's use the x-values.

#### Example:

Find three ordered pairs that satisfy the equation. Graph each equation.

y = x + 4

#### Solution:

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

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