Coordinate Plane

Before learning about two variable equations it's important to have a basic understanding of the coordinate plane.

The coordinate plane was developed centuries ago (in 1637, to be exact) and refined by the French mathematician René Descartes. In his honor, the system is sometimes called the Cartesian coordinate system. The coordinate plane can be used to plot points and graph lines. This system allows us to describe algebraic relationships in a visual sense, and also helps us create and interpret algebraic concepts.

The Components of the Coordinate Plane

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis. The point at which the two axes intersect is called the origin. The origin is at 0 on the x-axis and 0 on the y-axis.

Locations on the coordinate plane are described as ordered pairs. An ordered pair tells you the location of a point by relating the point’s location along the x-axis (the first value of the ordered pair) and along the y-axis (the second value of the ordered pair).

In an ordered pair, such as (x, y), the first value is called the x-coordinate and the second value is the y-coordinate. Note that the x-coordinate is listed before the y-coordinate. Since the origin has an x-coordinate of 0 and a y-coordinate of 0, its ordered pair is written (0, 0).

Example:

Find the point (4,3)

To identify the location of this point, start at the origin (0, 0) and move right along the x-axis until you are at 4. The 4 indicates that, from the origin, you have traveled four units to the right along the x-axis. This is the x-coordinate, the first number in the ordered pair.

From 4 on the x-axis move up 3 units as indicated by the y-coordinate. With an x-coordinate of 4 and a y-coordinate of 3, you have the ordered pair (4, 3).

Identifying Quadrants

The intersecting x- and y-axes of the coordinate plane divide it into four sections. These four sections are called quadrants. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counter clockwise.

Independent vs Dependent Variable

The names of the axes vary based on your application. The horizontal number line represents your independent variable and the vertical number line represents your dependent variable. The independent variable is the variable that causes a result, that is measured by the dependent variable.

Example 1
Identify the independent and dependent variables in the situations below.

a. The revenue, or amount of money a business earns from selling a product, versus the number of products sold

b. The number of hours versus the number of bacteria in a petri dish

Solution:
a. It is usually easier to identify the dependent variable. First, ask whether the number of products sold depends on the revenue OR whether the revenue depends on the number of products sold. Since the revenue depends on the number of products sold, the revenue is the dependent variable and the number of products sold is the independent variable.

b. Does the number of hours depend on the number of bacteria or does the number of bacteria depend on the number of hours? Since the number of bacteria depends on the elapsed time, the number of bacteria is the dependent variable and the number of hours is the independent variable.

Reference

Splashlearn: Coordinate Plane

Lumen: Beginning Algebra: Coordinate Plane

CK-12: The Coordinate Plane