# Graphs

## Graphing with Intercepts


### Identify the Intercepts on a Graph

Every linear equation has a unique line that represents all the solutions of the equation. When graphing a line by plotting points, each person who graphs the line can choose any three points, so two people graphing the line might use different sets of points.
At first glance, their two lines might appear different since they would have different points labeled. But if all the work was done correctly, the lines will be exactly the same line. One way to recognize that they are indeed the same line is to focus on where the line crosses the axes. Each of these points is called an intercept of the line.
Let’s look at the graph of the lines shown in .
First, notice where each of these lines crosses the x- axis: 
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 x-intercept of the line.  The x- intercept occurs when y is zero.
Now, let's look at the points where these lines cross the y-axis.

### Find the Intercepts from an Equation of a Line

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

### Graph a Line Using the Intercepts

To graph a linear equation by plotting points, you can use the intercepts as two of your three points. Find the two intercepts, and then a third point to ensure accuracy, and draw the line. This method is often the quickest way to graph a line. 

### Choose the Most Convenient Method to Graph a Line

While we could graph any linear equation by plotting points, it may not always be the most convenient method. This table shows six of equations we’ve graphed in this chapter, and the methods we used to graph them.
What is it about the form of equation that can help us choose the most convenient method to graph its line?
Notice that in equations #1 and #2, y is isolated on one side of the equation, and its coefficient is 1. We found points by substituting values for x on the right side of the equation and then simplifying to get the corresponding y- values. 
Equations #3 and #4 each have just one variable. Remember, in this kind of equation the value of that one variable is constant; it does not depend on the value of the other variable. Equations of this form have graphs that are vertical or horizontal lines.
In equations #5 and #6, both x and y are on the same side of the equation. These two equations are of the form . We substituted  and  to find the x- and y- intercepts, and then found a third point by choosing a value for x or y.  
This leads to the following strategy for choosing the most convenient method to graph a line.

### Key Concepts

1. Intercepts
2. Find the 
3. Graph a line using the intercepts
4. Choose the most convenient method to graph a line

### Practice Makes Perfect

Identify the Intercepts on a Graph 
In the following exercises, find the  and  intercepts.
Find the  
In the following exercises, find the intercepts.
Graph a Line Using the Intercepts 
In the following exercises, graph using the intercepts.
Choose the Most Convenient Method to Graph a Line 
In the following exercises, identify the most convenient method to graph each line.

### 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?
