Writing the Equation of a Line
Introduction to Writing the Equation of a Line in Slope-Intercept Form
Example: Write an equation of the line t in slope-intercept form.
The slope-intercept form of a linear equation is y = mx + b, where m represents that slope and b represents the y-intercept. The slope of line t is −13and the y-intercept is 2. Therefore, an equation of line t in slope-intercept form is y = −13x + 2.
In the following interactivity, you will explore how to write an equation of a line in slope-intercept form when given the slope and a point on the line, and when given two points on the line.
Writing the Equation of a Line in Slope-Intercept Form
To write an equation of a line in slope-intercept form, you must determine the slope and the y-intercept of the line. In this interactivity, you will learn how to write a linear equation in slope-intercept form when given the slope and a point on the line, and when given two points on a line. Click the player button to begin.
View a printable version of this interactivity.
Introduction to Writing the Equation of a Line in Point-Slope Form
Example: Write an equation of line p in point-slope form.
The point-slope form of a linear equation is y − y1 = m (x − x1), where m represents the slope and (x1, y1) represents a point on the line.
By analyzing the graph of line p, you find that the slope m is 34. There are an infinite number of points that lie on point p. The coordinates of one of these points is (4, 2). So, let (x1, y1) = (4, 2). You have enough information to write an equation of line p in point-slope form.
| y − y1 = m (x − x1) | |
y − 2 =34(x − 4) |
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In the following interactivity, you will explore how to write an equation of a line in point-slope form when given the slope and a point on the line, and when given two points on the line.
Writing the Equation of a Line in Point-Slope Form
When a linear equation is written in point-slope form, the slope and the coordinates of a point on the line are easily identifiable. As you work through the examples in this interactivity, you will learn how to write a linear equation in point-slope form when given the slope and a point on the line, and when given two points on the line. Click the player button to begin.
View a printable version of this interactivity.
Introduction to Writing the Equation of a Line in Standard Form
Example: Write an equation of line g in standard form.
The standard form of a linear equation is Ax + By = C, where
- A, B, and C are integers, and
- A and B are not both equal to 0.
To write an equation of line g in standard form, begin by first writing an equation in slope-intercept form or point-slope form. For example, in slope-intercept form, the equation of line g is y = −2x + 4.
Now use inverse operations to convert the equation of line g from slope-intercept form to standard form.
Add 2x to both sides of the equation:
| y = −2x + 4 | |||
| +2x | +2x | ||
| _____________________ |
| 2x + y = 4 |
An equation of line g in standard form is 2x + y = 4.
It is important to note that it is possible to write multiple equations in standard form to represent line g.
For example, multiply each term of 2x + y = 4 by 3:
| 3(2x + y = 4) |
| 6x + 3y = 12 |
Or multiply each term of 2x + y = 4 by 5:
| 5(2x + y = 4) |
| 10x + 5y = 20 |
The equations 2x + y = 4, 6x + 3x = 12, and 10x + 5y = 20 are equivalent. Each of the equations accurately represents line g.
In the following interactivity, you will explore how to write an equation of a line in standard form when given the slope and a point of the line, and when given two points on the line.
Writing the Equation of a Line in Standard Form
To write an equation of a line in standard form, it is helpful to begin by representing the equation in slope-intercept form or point-slope form. In this interactivity, you will apply your skills writing linear equations to write an equation of a line in standard form, when given the slope and a point on the line and when given two points on the line. Click the player button to begin.
View a printable version of this interactivity.
Writing The Equations of Horizontal and Vertical Lines
Example: Write the equation of a line that passes through the point (1, 3) and has a slope of 0.
Because the line has a slope of 0, you can conclude that it is horizontal. Recall that the equation of a horizontal line is defined by its constant y-value.
From the given point (1, 3), you can determine that the constant y-value is 3. Therefore, the equation of the line is y = 3.
Example: Write the equation of a line that passes through the point (1, 3) and has an undefined slope.
Because the line has an undefined slope, you can conclude that it is vertical. Recall that the equation of a vertical line is defined by its constant x-value.
From the given point (1, 3), you can determine that the constant x-value is 1. Therefore, the equation of the line is x = 1.
Practical Problem
Example: The initial fee to activate cable television service with a local provider is $32. The provider then charges $50 for each month of service. Write an equation in slope-intercept form to represent the total cost of cable service.
In this example, the total cost depends on the number of months a customer is provided cable television. So, the independent variable x is the time in months and the dependent variable y is the total cost.
The constant rate for service is $50 per month. In addition, the provider charges an initial fee of $32 to activate service. Therefore, this situation can be modeled by the equation y = 50x + 32.
Writing the Equation of a Line Review
Now that you have learned how to write the equation of a line, it is time to test your knowledge. This interactivity will help you review the information covered throughout this topic. Click the player button to get started.
Did you answer the content review questions incorrectly? Do you want more instruction or extra practice? If so, view the videos Writing the Equation of a Line When Given a Graph, Writing the Equation of a Line When Given the Slope and Point on the Line, and Writing the Equation of a Line When Given Two Points on the Line from eMediaVASM.