Study Guide

Basic Algebra - Graphing xy Points

Graphing xy Points

Chances are, we've been graphing points for a long time. However, we've probably been doing so on charts that look like this:

graph

But since we're blasting ahead in math, we'll soon be graphing on charts that look like this:

graph 2

This is called a Cartesian coordinate graph. It's made up of two axes ("axes" is just the plural of "axis"):

  • The horizontal axis is called the x-axis. 
  • And the vertical one is the y-axis

graph 3

When the two axes meet, they form four quadrants. These are labeled as Quadrants I, II, III, and IV (usually shown in Roman numerals) and are ordered counterclockwise starting from the upper-right quadrant.

quadrants

Plotting Points on a Graph

Cartesian points are written as xy pairs in parentheses, like so: (x, y). To graph a point, first locate its position on the x-axis, then find its location on the y-axis, and finally plot where these meet.

The center point of the graph is called the origin and is written as the point (0, 0) because it's located at the zero point on the x-axis and the zero point on the y-axis.

For example, to plot the point (3, -6), find the positive 3 on the x-axis and the negative 6 on the y-axis.

graph 4

Practice makes perfect, so let's give the Cartesian coordinates of each point and name the quadrant they lie in, using the graph below.

points in graph

A. (5, 3), Quadrant I
B. (-3, 1), Quadrant II
C. (-6, -4), Quadrant III
D. (0, -3). It lies on an axis so it's not in a quadrant.
E. (0, 0). No quadrant because it's at the origin.
F. (4, -5), Quadrant IV
G. (6.5, 0). It lies on an axis so it's not in a quadrant.