Math Background

Coordinate Graphing: Overview

Coordinate graphing sounds very dramatic, but it is actually just a visual method for showing relationships between numbers. The relationships are shown on a coordinate grid. A coordinate grid has two perpendicular number lines, or axes. The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the x-axis and y-axis intersect is called the origin.

coordinate grid

The numbers on a coordinate grid are used to locate points. Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. Ordered pairs are written in parentheses (x-coordinate, y-coordinate). The origin is located at (0, 0).

The location (2, 5) is shown on the coordinate grid below. The x-coordinate is 2. The y-coordinate is 5. To locate (2, 5), start at (0, 0), then move 2 units to the right on the x-axis and 5 units up on the y-axis.

coordinate grid

The order in which you write x- and y-coordinates in an ordered pair is very important. The x-coordinate always comes first, followed by the y-coordinate. As you can see in the coordinate grid below, the ordered pairs (3, 4) and (4, 3) refer to two different points.

coordinate grid

The function table below shows the x- and y-coordinates for five ordered pairs. You can describe the relationship between the x- and y-coordinates for each of these ordered pairs with this rule: The x-coordinate plus two equals the y-coordinate. You can also describe this relationship with the algebraic equation x + 2 = y.

x-coordinate x + 2 = y y-coordinate Ordered Pair
0 0 + 2 = 2 2 (0, 2)
1 1 + 2 = 3 3 (1, 3)
2 2 + 2 = 4 4 (2, 4)
3 3 + 2 = 5 5 (3, 5)
4 4 + 2 = 6 6 (4, 6)

To graph the equation x + 2 = y , each ordered pair is located on a coordinate grid, and then the points are connected. Notice that the graph forms a straight line. The arrows indicate that the line goes on in both directions. The graph for any simple addition, subtraction, multiplication, or division equation forms a straight line.

coordinate grid

Houghton Mifflin Math Grade 4