We have seen how linear inequalities are graphed on a number line.
Let's take a look at how those number line graphs correspond to coordinate axes graphs.

bullet Solve x + 2 < 0
We know that this inequality simplifies to x < -2, and that its number line graph looks like:

circlegraph20

bullet Now, let's look at its connection to the two-variable graph y = x + 2.

The inequality x + 2 < 0 can also be thought of as asking "when is the line y = x + 2 below (less than) the line y = 0.

Since y = 0 is the x-axis, this example is looking for when the line y = x + 2 is below (less than) the x-axis.

The x-intercept occurs when x = -2, and the line y = x + 2 is below y = 0 to the left of the point (-2,0). The solution is the x-values less than -2 (written x < -2).

A graphing calculator displays inequalities in this same manner.

qgraph2
qgraph3 The graphing calculator plots a y-value of "1" for all of the x-values that will make the inequality true, and a "0" for all of the x-values that will make the inequality false.

You may not see the "0" plots since they lie on top of the x-axis. The graphing calculator will not place an open circle at x = -2, but the table feature will show that the x = -2 is not a solution.

Understanding the connection between number line graphs and their associated coordinate axes graphs will come in handy when working with quadratic inequalities.



divider


NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation
 and is not considered "fair use" for educators. Please read the "Terms of Use".

Topical Outline | Algebra 1 Outline | MathBitsNotebook.com | MathBits' Teacher Resources
Terms of Use    Contact Person: Donna Roberts

Copyright © 2012-2025 MathBitsNotebook.com. All Rights Reserved.