Graphing Inequalities

I.  Homework

II.  Linear Inequalities

A linear inequality is an inequality of the form

Ax + By < C,  Ax + By > C,  Ax + By < C, or Ax + By >C

We follow the follow the procedure listed below to graph the inequality:

Step 1

Write a T-table plotting the x and y intercepts (find where x = 0 and where y = 0).  If the equation gives (0,0) as a point, plot another convenient point such as when x = 1.

Step 2

Plot the two points on the xy-plane

Step 3

If the inequality is "<" or ">" then connect the two points with a dotted line.  The dotted line is analogous to the open circle on the number line.

Otherwise, connect the two points with a solid line. The solid line is analogous to the closed disk on the number line.  

Step 4

If (0,0) is not on the line, substitute (0,0) into the inequality to see if it is true for (0,0).

If it is true, shade the half plane that includes (0,0).  If the inequality is false for (0,0), then shade the half plane that does not include (0,0).

If (0,0) is on the line, then follow the same procedure using (1,0) or (0,1) whichever is not on the line.

Example:

2x - y < 2

1)  We have

x	y
0	-2
1	0

2)  We plot the points (0,-2) and (1,0) on the number line.

3)  Since the inequality is "<", we connect the points with a dotted line.

4)  (0,0) is not on the line.  We test:

2(0) - (0) < 6 or 0 < 6

Since this statement is true, we can shade in the half plane containing (0,0).  This is the half plane above the dotted line.

The class will try the following examples.

2x + y > 10

x + y < 2

x + 4 > 2

y - 6 < 1