Interesting Intercepts: x and y

Lesson Plan - Get It!

Audio:

The coordinate plane is made up of an x axis and y axis, with the x axis running side to side horizontally, and the y axis running up and down vertically.

The point where these two cross is called the origin, and it is found at (0,0) on the graph. So, what are the points that land on each axis? They each have a special name, and as you move forward in your math lessons, you will see that they are very important.

The point where a graph crosses the x-axis is called the x-intercept. Its ordered pair will always be a number first, then 0 Examples: (2,0), (-6,0), (100,0)

The point where a graph crosses the y-axis is called the y-intercept. Its ordered pair will always be a 0 first, then a number. Examples: (0,3), (0,-8), (0,50)

You can find these interesting intercepts fairly quickly when looking at a graph. You should be concerned with where the line crosses the x or y axis and, once found, you can name that point.

Example:

1. Grab a piece of paper and draw a coordinate plane.
2. Put two different straight lines on it.
3. Take a minute to find and label each intercept. Remember, you are just looking for where each line crosses the x and y axis.
4. The ordered pair for the x-axis will always be the number where it is located and 0, and the ordered pair for the y-axis will always be 0 and the number where the point is located.

Lines on the coordinate plane have equations that go with them, so there will be times when you are given the equation of the line but not the graph itself. With just the equation, you can find the intercepts. Once you have the intercepts, it is a piece of cake to graph each of them, then draw the line if needed.

Example: Find the x and y intercept for the equation 2x + 4y = 6.

You could now graph this line by plotting the x-intercept at (3,0) and the y-intercept at (0,³⁄₂).

As you can see from the example, there may be times you get a fraction. That is COMPLETELY OK! You can change the fraction to a decimal by taking the numerator divided by the denominator. In this case, that would be 3 ÷ 2 = 1.5. You could now place your point at (0,1.5).

Take a minute and graph this line on your piece of paper.

1. First, draw your y intercept by going "up" to 1.5 on the y-axis.
2. Label it as (0,1.5).
3. Then, draw the point (3,0) by going over to 3 on the x-axis. Be sure to label it accordingly.
4. Then, connect the dots with a straight line. You can put arrows on each end to show that they would continue going infinitely in each direction.

That's it! You have found the x and y intercepts when given an equation, and graphed it.

Here is one more example for finding the intercepts and plotting them on the graph. Please watch How to Find the X and Y Intercept of a Line (Example 1) Intermediate Algebra, Lesson 60 by Learn Math Tutorials to review just what to do:

Let's see just how well you are understanding how to find the intercepts by moving to the Got It? section.