**Graphing a Line using the x and y Intercepts**

Another excellent method to graph a line in the xy axis is to use its **intercepts**. What are intercepts? These are points of the line that are found on the axis itself. We have two kinds of intercepts.

- The first one is called the
**x-intercept**because it is the point of the line located somewhere in the horizontal axis (x-axis). - The second is the
**y-intercept**which is the point of the line located somewhere in 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!

**Example 1:** Graph the equation of the line **2 x – 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 in 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.