# Inequalities - Regions of Graphs

This applet investigates graphing linear inequalities, finding regions of graphs defined by systems of straight line (linear) inequalities

###### Author and programmer: Ron Barrow

UK Years 10-12, KS4, KS5, Higher GCSE, AS Decision (Discrete) Mathematics 1 - Algebra and Graphs

Instructions below       See also:    Simple Inequalities    Line Graphs - ax + by = c    Print

## How to Use this Applet

This applet is designed to help you understand the regions of graphs described by inequalities, such as:

You can look at one, two or three regions at the same time, by clicking the tick boxes at the top of the page.
The lines which define the regions can be changed by clicking the buttons at the bottom of the page.
• Line 1 has equation: Ax + By = C
• Line 2 has equation: Dx + Ey = F
• Line 3 has equation: Gx + Hy = I

Also at the bottom are three drop-down menus (in between the buttons) which enable you to change the type of inequality.
If you tick next to "Integer points" at the top of the screen, the region defined by the inequality or inequalities is marked with small circles. The circles all lie on integer points (points whose coordinates are all integers (whole numbers)).
If you then tick next to "Positive points" at the top of the screen, the region defined by the inequality is restricted to non-negative values for x and y.
Have fun! Learn by playing around!