# X-Axis: Definition & Overview

Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

In this lesson, you'll learn about the x-axis. How does it relate to a number line? What does it mean if a point falls right on the x-axis? Find out why the x-axis is important in graphing two or more dimensions.

## Definition

On a Cartesian plane, a two-dimensional mathematical graph, the x-axis is like a number line. It tells you the x coordinate for any point. When you look at a two-dimensional graph, you can find the x value for a point by using the x-axis to indicate how far that point is to the right or the left of the origin (the point where x = 0 and y = 0).

## Airplane Runways

Imagine you are driving an airplane along a runway. The airplane's starting point is labeled '0.' At the '1' you've driven 100 feet, at the '5' you've driven 500 feet, and so forth. If you backed up the plane, you would end up at a negative number. The airplane below is on about the '2.'

This runway might look a bit like a number line from math class. It's a one-dimensional graph. It can measure distances frontwards and backwards but not sideways or up and down. Let's call the direction the airplane is traveling on the runway the x direction. Of course, a plane can travel in three dimensions, but the picture above assumes the airplane is confined to the runway.

The truth is that even if the airplane is flying directly above the runway, you can use the number line to indicate where it is in the x (horizontal) direction. The airplane is now traveling in two dimensions, but the number line only tracks the x direction. The airplane is at x = 2. If you move the airplane even higher up into the sky, it is still at x = 2. Once you allow the airplane to start moving vertically, the number line changes names. It is now called the the x-axis.

If you want to track how high the airplane is, you need to measure the vertical, or y, direction, too. The easiest way to indicate where the plane is at all times in two directions is to create a grid. Of course, drawing in the actual grid isn't really necessary. Using a horizontal measuring stick (x-axis) and a vertical measuring stick (y-axis) is enough. Below, you can see that the airplane is at about x = 2 and y = 4.

You might be wondering whether you can also track where the airplane is in a third direction, the sideways or front/back direction. Doing so is easy in theory but a little hard to show on a flat sheet of paper. Imagine a measuring stick coming straight out at you from the front of your computer screen. That is the z-axis, and it lets you indicate the airplane's position in all three dimensions at once.

## Crossing the x-axis

One common task in math classes is to find where a line or curve touches, or crosses, the x-axis. Of course, you can only cross the x-axis if negative numbers make sense in the y direction. For the airplane, you might imagine that at some point the airplane flies over a large ravine or valley. If the airplane descends into the ravine, even briefly, then the y-coordinate (value) is negative. The plane was below its starting point at ground level.

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