Week 11 – Graphing Linear Inequalities in Two Variables

To graph a linear inequality in two variables, identify the slope and the y-intercept by making it into the form of y = mx + b.

For example:  -5 < 2x – y

Change it so y is alone on one side —> y < 2x + 5

The slope is 2 and the y-intercept is 5.

The graph of  y = 2x + 5 looks like this:

A solid line means  or  and a broken line means > or <. This graph will have a broken line through the points because it is not part of the region defined by in the inequality.

Choose a test point that is not on the line to determine which region to shade.

Let’s choose (0,0) as a test point. Substitute x = 0 and y = 0 in  y < 2x + 5.

0 < 5. This statement is true, so shade the side of the line that has the point (0,0).