# Graphing a Line using the x and y-Intercepts

Another method to graph a line in the XY-plane is to use the intercepts. What are intercepts? These are points of the line that are found on the \color{red}\large{x} and \color{red}\large{y} axes. There are 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.

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