# The coordinate plane

As you remember from pre-algebra a coordinate plane is a two-dimensional number line where the vertical line is called the y-axis and the horizontal is called the x-axis. These lines are perpendicular and intersect at their zero points. This point is called the origin. The axes divide the plane into four quadrants.

A point in a coordinate plane is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinates and the second to the y-coordinate.

The completeness property for points in the plane tells us two things

- Exactly one point in the plane is named given the numbers of the ordered pair and
- Exactly one ordered pair of numbers names a given point in the plane.

To graph a point one draws a dot at the coordinates that corresponds to the ordered pair. It's always a good idea to start at the origin. The x-coordinate tells you have many steps you have to take to the right (positive) or left (negative). And the y-coordinate tells you have many steps to move up (positive) or down (negative).

To find out the coordinates of a point in the coordinate system you do the opposite. Begin at the point and follow a vertical line either up or down to the x-axis. There is your x-coordinate. And then do the same but following a horizontal line to find the y-coordinate.

A relation is a set of ordered pairs. The first coordinate (usually the x-coordinate) is called the domain and the second (usually the y-coordinate) is called the range. If you remember from earlier chapters the domain contains values that correspond to the independent variable whereas the range contains values corresponding to the dependent variable.

**Video lesson**

Draw the following ordered pairs in the coordinate plane

(0, 0); (0,4); (4, -2); (-2, -4); (1, 3)