# Graphs

## Graph with Intercepts


### Identify the x- and y- Intercepts on a Graph

Every linear equation can be represented by a unique line that shows all the solutions of the equation. We have seen that when graphing a line by plotting points, you can use any three solutions to graph. This means that two people graphing the line might use different sets of three points.
At first glance, their two lines might not appear to be the same, since they would have different points labeled. But if all the work was done correctly, the lines should be exactly the same. One way to recognize that they are indeed the same line is to look at where the line crosses the x- axis and the y- axis. These points are called the intercepts of the line.
Let’s look at the graphs of the lines in .
First, notice where each of these lines crosses the  negative axis. See .
Do you see a pattern?
For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form  and is called the . The x- intercept occurs when  is zero.
Now, let’s look at the points where these lines cross the y- axis. See .
What is the pattern here?
In each row, the x- coordinate of the point where the line crosses the y- axis is zero. The point where the line crosses the y- axis has the form  and is called the y- intercept of the line. The y- intercept occurs when  is zero.

### Find the x- and y- Intercepts from an Equation of a Line

Recognizing that the  occurs when y is zero and that the y- intercept occurs when x is zero, gives us a method to find the intercepts of a line from its equation. To find the x- intercept, let  and solve for x. To find the , let  and solve for y.
 

### Graph a Line Using the Intercepts

To graph a linear equation by plotting points, you need to find three points whose coordinates are solutions to the equation. You can use the x- and y- intercepts as two of your three points. Find the intercepts, and then find a third point to ensure accuracy. Make sure the points line up—then draw the line. This method is often the quickest way to graph a line.
The steps to graph a linear equation using the intercepts are summarized below.

### Key Concepts

1. Find the 


2. Graph a Linear Equation using the Intercepts


3. Strategy for Choosing the Most Convenient Method to Graph a Line:



### Practice Makes Perfect

Identify the 
In the following exercises, find the x- and y- intercepts on each graph.
Find the 
In the following exercises, find the intercepts for each equation.
Graph a Line Using the Intercepts
In the following exercises, graph using the intercepts.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?