# 3.5: Graphs of Linear Functions from Intercepts

Difficulty Level: At Grade Created by: CK-12

What are the intercepts of ? How could you use the intercepts to quickly graph the function?

### Guidance

To graph a linear function, you need to plot only two points. These points can then be lined up with a straight edge and joined to graph the straight line. While any two points can be used to graph a linear function, two points in particular that can be used are the -intercept and the -intercept. Graphing a linear function by plotting the and intercepts is often referred to as the intercept method.

The -intercept is where the graph crosses the -axis. Its coordinates are . Because all -intercepts have a coordinate equal to 0, you can find an -intercept by substituting 0 for in the equation and solving for .

The -intercept is where the graph crosses the -axis. Its coordinates are . Because all -intercepts have a coordinate equal to 0, you can find an -intercept by substituting 0 for in the equation and solving for .

#### Example A

Identify the and -intercepts for each line.

(a)

(b)

Solution:

(a)

(b)

#### Example B

Use the intercept method to graph

Solution:

#### Example C

Use the and -intercepts of the graph to identify the linear function that matches the graph.

The -intercept is (-8, 0) and the -intercept is (0, 4).

Solution:

This does not match the graph. This does not match the graph. Confirm the -intercept.

The -intercept is (0, 4). This matches the graph.

The linear function that matches the graph is

#### Concept Problem Revisited

The linear function can be graphed by using the intercept method.

Plot the -intercept on the -axis and the -intercept on the -axis. Join the two points with a straight line.

### Vocabulary

Intercept Method
The intercept method is a way of graphing a linear function by using the coordinates of the and -intercepts. The graph is drawn by plotting these coordinates on the Cartesian plane and joining them with a straight line.
-intercept
A -intercept of a relation is the coordinate of the point where the relation intersects the -axis.
-intercept

A -intercept of a relation is the coordinate of the point where the relation intersects the -axis.

### Guided Practice

1. Identify the and -intercepts of the following linear functions:

(i)
(ii)

2. Use the intercept method to graph the following relation:

(i)

3. Use the and -intercepts of the graph, to match the graph to its function.

(i)
(ii)
(iii)

Answers:

1. (i)

If you prefer to have both variables on the same side of the equation, this form may also be used. The choice is your preference.

(ii)

2. Determine the and -intercepts.

3. Identify the and -intercepts from the graph.

The -intercept is (3, 0)

The -intercept is (0, -4)

Determine the and -intercept for each of the functions. If the intercepts match those of the graph, then the linear function will be the one that matches the graph.

(i)

(ii)

(iii)

### Practice

For 1-10, complete the following table:

Function -intercept -intercept
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.

Use the intercept method to graph each of the linear functions in the above table.

Use the and -intercepts to match each graph to its function.

a.
b.
c.
d.

### Notes/Highlights Having trouble? Report an issue.

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Date Created:
Dec 19, 2012
Last Modified:
Apr 29, 2014

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