1. Graphing Linear Inequalities in 2 Variables

2. Checking Solutions 3x + 2y ≥ 2
An ordered pair (x,y) is a solution if it makes the inequality true.
Are the following solutions to:
3x + 2y ≥ 2
(0,0) (2,-1) (0,2)
3(0) + 2(2) ≥ 2
4 ≥ 2
Is a solution
3(0) + 2(0) ≥ 2
0 ≥ 2
Not a solution
3(2) + 2(-1) ≥ 2
4 ≥ 2
Is a solution

3. To sketch the graph of a linear inequality:
Sketch the line given by the corresponding equation (solid if ≥ or ≤, dashed if < or >) This line separates the coordinate plane into 2 half-planes.
2. In one half-plane – all of the points are solutions of the inequality.
In the other half-plane - no point is a solution
3. You can decide whether the points in an entire half-plane satisfy the inequality by testing ONE point in the half-plane.
4. Shade the half-plane that has the solutions to the inequality.

4. Graphing an Inequality in Two Variables
Graph x < 2
Step 1: Start by graphing the line x = 2
Now what points would give you less than 2?
Since it has to be x < 2 we shade everything to the left of the line.

5. Graphing a Linear Inequality
Sketch a graph of y  3

6. Step 1: Put into slope intercept form
Using What We Know
Sketch a graph of x + y < 3
Step 1: Put into slope intercept form
y <-x + 3
Step 2: Graph the line y = -x + 3

7. The graph of an inequality is the graph of all the solutions of the inequality
3x+ 2y ≥ 2
y ≥ -3/2x + 1
(put into slope-intercept form to graph easier)
Graph the line that is the boundary.
Before you connect the dots check to see if the line should be solid or dashed
solid if ≥ or ≤
dashed if < or >

8. y ≥ -3/2x + 1 Step 1: graph the boundary (the line is solid ≥)
Step 2: test
a point NOT
On the line
(0,0) is always
The easiest if it’s
Not on the line!!
3(0) + 2(0) ≥ 2
0 ≥ 2
Not a solution
So shade the other side of the line!!

9. Graph: y < 6

10. y < 3x - 2

11. 4x – 2y < 7