# 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!

**Rules 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 **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 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.