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Basic Algebra

Basic Algebra

At a Glance - Graphing X-Y Points

Graphing X-Y Points

Chances are you have been graphing points for a long time. However, you may have been doing so on charts that look like this:


But since you are blasting ahead in math, you will soon be graphing on charts that look like this:

graph 2

This is called a Cartesian coordinate graph. It is made up of two axes ("axes" is simply 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 1-4 (usually shown in Roman numerals) and are ordered counterclockwise starting from the upper-right quadrant.


Plotting Points on a Graph

Cartesian points are written as x-y pairs, in parentheses (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 is 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 three on the x-axis and the negative six on the y-axis.

graph 4

Give the Cartesian coordinates of each point and name the quadrant they lie in.

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 is not in a quadrant
E. (0, 0), no quadrant
F. (4, -5), Quadrant IV
G. (6.5, 0), it lies on an axis so it is not in a quadrant

Here are some video examples of math in action. Keep on practicing.


Exercise 1

In which quadrant(s) are both the x and y coordinates the same sign?

Exercise 2

If a point has a y coordinate of zero, which axis does it lie on?

Exercise 3

Do these points lie in a straight line: (-8, -1), (-6, 1), (-4, 3) and (0, 7)?

Exercise 4

What type of quadrilateral do these points form: (-3, 1), (4, 1), (2, -2) and (-5, -2)?

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