## 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

**The point where the**

*y-axis.**x-axis*and

*y-axis*intersect is called the

**origin.**

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

**Ordered pairs are written in parentheses (**

*y-coordinate.**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.*

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.

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.