Using the X and Y Intercept to Graph Linear Equations

You've learned one way to graph a standard form equation - by converting it to slope intercept form. Click here to review this lesson.

There is another way to graph standard form equations, and that is to find the x and y intercepts.

Now let's review what the term intercepts means. An intercept is where your line crosses an axis. We have an x intercept and a y intercept.

The point where the line touches the x axis is called the x intercept. The point where the line touches the y axis is called the y intercept.

Take a look at the graph below.

Definition of Intercepts

If we can find the points where the line crosses the x and y axis, then we would have two points and we'd be able to draw a line.

When equations are written in standard form, it is pretty easy to find the intercepts. Take a look at this diagram, as it will help you to understand the process.

Now, let's apply this. Just remember:

To find the X Intercept: Let y = 0

To find the Y Intercept: Let x = 0

Example 1: Graphing a Standard Form Equation

Graphing Standard Form Equations Using Intercepts

This concept can be confusing, so let's take a look at the video to explain the first example.

Ok.. now let's look at a real world problem that we can solve using intercepts.

Example 2: Solving Real World Problems

Emily received a gift card for her birthday and decided to download a few books. She downloaded a few $6 books and a few $3 books. She spent $30 on books. The equation that represents x number of $6 books and y number of $3 books is:

6x + 3y = 30

  • Graph the equation.
  • Find the x-intercept. Explain what the x-intercept means in the context of this problem.
  • Suppose Emily downloaded 3 $6 books. How many $3 books did she download?


The x-intercept is (5,0). The x-intercept means that if no $3 books are purchased, Emily could purchase 5, $6 books for $30.

By reading our graph, we see that if Emily bought 3, $6 books, she could buy 4, $3 books.

Let's prove it!

6x + 3y = 30

6(3) + 3(4) = 30

18 + 12 = 30

30 = 30

It works!  Therefore, (4,3) is a solution to this problem.

Great job on graphing equations.

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