Graphing a Line using the x and y-Intercepts
Another excellent method to graph a line in the xy-axis or xy-plane is to use its intercepts. What are intercepts? These are points of the line that are found on the x and y axes. We have two kinds of intercepts.
- The first one is called the x-intercept because it is the point of the line located on the horizontal axis (x-axis).
- The second is the y-intercept which is the point of the line located on the vertical axis (y-axis).
Here is a quick diagram that gives you the idea.
Since the x-intercept is a point where the line crosses the x-axis, it is a point with a y-value of zero.
In the same manner, since the y-intercept is a point where the line crosses the y-axis, it must be a point with an x-value of zero.
Using the informal definitions of x and y-intercepts above, it makes a lot of sense why the procedures below on how to find them work!
Rules on How to Find the Intercepts
- To find the x-intercept:
Let y = 0 in the equation, then solve for x.
- To find the y-intercept:
Let x = 0 in the equation, then solve for y.
Examples of How to Graph a Line using the x and y-intercepts
Example 1: Graph the equation of the line 2x – 4y = 8 using its intercepts.
I hope you recognize that this is an equation of a line in Standard Form where both the x and y variables are found on one side of the equation opposite the constant term. It is a common practice in an algebra class to ask students to graph the line using the intercept method when the line is in Standard Form.
Here we go!
- To find the x-intercept:
Let y = 0 in the equation, then solve for x.
The x-intercept is (4, 0).
- To find the y-intercept:
Let x = 0 in the equation, then solve for y.
The y-intercept is (0, –2).
Now we can plot the two points on the xy axis and connect them using a straight edge ruler to show the graph of the line.
Example 2: Graph the equation of the line using its intercepts.
This equation of the line is in the Slope-Intercept Form. We can actually graph this using another technique which uses the slope and the y-intercept taken directly from the equation. You can see a separate tutorial here.
Since this lesson is about intercepts, let’s work this out using this method.
- To find the x-intercept:
Let y = 0 in the equation, then solve for x.
The x-intercept is (–2, 0).
- To find the y-intercept:
Let x = 0 in the equation, then solve for y.
The y-intercept is (0, 3).
Plot the intercepts in the axes and draw a straight line passing through them using a ruler.
You might also be interested in:
Three Ways to Graph a Line
Graphing a Line using Slope and y-intercept
Graphing a Line using Table of Values