Y-Axis: Definition

Y-Axis: Definition & Overview

The y-axis is the vertical 'ruler' on a Cartesian plane, a two-dimensional graph. Learn why it is important in mathematical graphing and how it relates to describing vertical and horizontal distances.

Definition

Imagine you want to measure an object's location vertically using a ruler. The y-axis is like a vertical ruler. It shows you where an object on a Cartesian plane, a two-dimensional mathematical graph, is in the y(vertical) direction. It is also the starting, or zero, point for measuring how far a point is to the right or left (horizontally) on a graph.

Vertical Distances and the y-axis

Suppose you work on the eighth floor of an office building. The elevator can take you up and down to any floor. In fact, someone could figure out what floor you worked on by watching where you got off the elevator.

In the vertical direction, you work at level 8. In math, the vertical direction is usually called y. So, your office is at y = 8.

Now, unless you are an elevator operator, you don't work right at the elevator. You might work down a hallway somewhere. But, the elevator is the access point to the various floors. Your office on the eighth floor is generally thought of as some distance from the elevator. The elevator is the zero point, or center, of the eighth floor. If you imagine the 20-floor skyscraper you work in, the elevator cuts vertically directly through all 20 floors. It is the orienting line through the center of the building.

Imagine that the eighth floor has one long hallway that extends east-west. One way to describe where your office is on the eighth floor is to say you are six offices east of the elevator. Someone who worked on the elevator would describe their office as being zero away from the elevator. The elevator is the zero point when measuring east-west.

When graphing on a Cartesian plane, the vertical orienting line is called the y-axis. Like the elevator, it tells you how high or low you are. But, also like the elevator, the y-axis is the place from which you measure your location horizontally (right-left or east-west).

On the graph below, the red dot is at x = -3 and y = 2. The y-axis shows you how high to go to find the value (2). But it is also the starting point for finding the x-value (-3). The point is three units to the left of the y-axis.

Cartesian plane

Crossing the y-axis

Instead of just graphing points, you might graph a line or a curve. In many cases, the line or curve will cross over the y-axis.

y-intercept

The place where the curve crosses the y-axis is called the y-intercept. It is also the place where x = 0. In the graph above, the y-intercept is at y = 2. Another way to say this is that x = 0 when y = 2.

If you imagine the elevator again, if you are at the elevator, then your distance in the east-west direction is 0. The elevator, like the y-axis is the orienting or zero-point.

The elevator's main floor entrance in a building is like the origin on a Cartesian plane, the crossing point of the x-axis and the y-axis. It is the orienting or zero-point, and just like going up and down in the elevator moves you along the y-axis, walking east or west of the elevator moves you along the x-axis.

Lesson Summary

The y-axis shows you where a point is on the is in the y (vertical) direction on a Cartesian plane. It's also the starting (zero) point used to determine how far a point is along the x-axis.