1. Graphing Inequalities
Eric Hoffman
Algebra II
PLHS
Sept. 2007

2. Key Topics
Graphing Inequalities: to graph an inequality you graph “boundary line” then shade the appropriate region
Boundary Line: the line that is the boundary for the shaded region
Boundary Line

3. Key Topics
If the inequality is a “≤” or “≥” then the boundary line is solid
If the inequality is a “<” or “>” then the boundary line is dashed

4. Steps For Graphing an Inequality
Step 1: Determine whether the boundary line is dashed or solid
Step 2: Graph the boundary line
Step 3: Choose a point on either side of the boundary line and check to see if the values satisfy the inequality
Step 4: Shade the side of the boundary line that satisfies the inequality

5. Graphing an Inequality
Graph the inequality 2x + 3y > 6
3y > -2x + 6
y > (-2/3)x + 2
Graph: y = (-2/3)x + 2
Choose any point:
(3,3)
3 > (-2/3)(3) + 2
2 > (-2) + 2
2 > 0
Tells us the boundary line is dashed
(3,3) is just a random point
This is true, so we shade the side of the boundary line that this point is on

6. True, so shade this region
Key Topics
Graph the inequality 3y + 6x ≥ 9
y ≥ -2x + 3
Check point:
(2,1)
1 ≥ -2(2) + 3
1 ≥ -1
y = -2x + 3
True, so shade this region

7. Graphing Absolute Value Inequalities
Same method as graphing regular inequalities
The graph of the absolute value of a linear equation will always look like a “V”
If you have trouble graphing absolute values, just plot points by picking different values for x

8. Absolute Value Inequality
There are basically two regions, region 1 is all the points where y is greater than, and region 2 is all the points where y is less than 1
y = | x – 1| 2 2

9. (0,3) satisfies the inequality, so shade this region
Key Topics
Graph
y ≥ | 3x + 2 |
Boundary line: y = | 3x + 2 |
Choose a point: (0,0)
Choose another point: (0,3)
(0,0) doesn’t satisfy the inequality so you can’t shade the region that it is in
y = | 3x + 2 |
(0,3) satisfies the inequality, so shade this region

10. Homework Pg. 98 14 – 28 even, 32 – 37 all 14 problems
You will need graph paper (provided)