The Equation of a Line Study Guide
Introduction to The Equation of a Line
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.
Determine if the ordered pairs satisfy the linear equation 2x – y = 4.
- (2,2) Solution: 2x – y = 4
- (0,–4) Solution: 2x – y = 4
2(2) – 2 4
4 – 2 4
2 ≠ 4
no; (2,2) is not on the line 2x – y = 4.
2(0) – (–4) 4
0 + 4 4
4 = 4
yes; (0,–4) is on the line 2x – y = 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.
Find three ordered pairs that satisfy the equation. Graph each equation.
- y = x + 4
Practice problems for these concepts can be found at: The Equation of a Line Practice Questions.
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