1. . Solve the inequality. Then graph the solution. 9 ≤ + – 4x 7 12x 1.
ANSWER 1 2 3 . 4 6 5 – ≥ x + 2.
2x or 3x
<
>
ANSWER
x < 4 or x > 2 – 2 4 6 8 10

2. 4.2 Solving Linear Inequalities in 2 Variables
10/16/2013

3. In this section, we’re going to graph inequalities written in:
Slope Intercept Form:
y > mx + b, y < mx + b, y ≥ mx + b, y ≤ mx + b
Standard Form:
Ax + By > C, Ax + By < C, Ax + By ≥ C, Ax + By ≤ C
A point (x , y) is a solution if and only if the inequality is TRUE when the value of x and y are substituted into the inequality.

4. Check whether the given ordered pair is a solution of . < 2x y + 5
Example 1
Check Solutions of Inequalities
Check whether the given ordered pair is a solution of .
<
2x y + 5 ( )
1, 4 a. b.
2, 1 ( ) –
ORDERED PAIR
SOLUTION a. ( )
1, 4
SUBSTITUTE ( )
1, 4
is not
a solution.
CONCLUSION
2 1 +4<5
2+4<5
6<5
2 2 +(−1)<5
4−1<5
3<5
2, 1 ( ) – b.
2, 1 ( ) –
is a
solution.

5. Check whether the given ordered pair is a solution of 4. > x 3y –
Checkpoint
Check Solutions of Inequalities
Check whether the given ordered pair is a solution of 4.
>
x y – ( )
0, 0 1.
ANSWER
not a solution 2.
4, 1 ( ) –
ANSWER
solution 3.
2, 2 ( ) –
ANSWER
not a solution 4.
3, 5 ( ) –
ANSWER
solution

6. Graphing a Linear Inequality Written in Slope-Intercept Form (y<mx+b)
1.) Draw the boundary line: y=mx+b
For > or <, dashed line
For ≤ or ≥, solid line
2.) Shade the half plane.
Shade above: > or ≥
Shade below: < or ≤
Above
Above
Boundary line
Boundary line
Below:
Below
Positive Slope
Negative Slope

7. Graphing a Linear Inequality Written in Standard Form (Ax+By>C)
1.) Draw the boundary line using the cover up method
For > or <, dashed line
For ≤ or ≥, solid line
2.) Shade the half plane.
Test a point (x, y) not on the boundary line and see if it is a solution. If it is a solution, shade the side that contains that point. If it is not a solution, shade the other side.

8. Example 2
Graph Linear Inequalities in Two Variables
Graph.
Dashed Line
Shade below
2x+2 y
< 8

9. Use the cover up method to make the boundary line 3𝑥=8 𝑥= 8 3 =2. 6
Example 3
Graph Linear Inequalities in Two Variables
Graph – 8 3x 2y ≥
Use the cover up method to
make the boundary line
3𝑥=8
𝑥= 8 3 =2. 6
−2𝑦=8
𝑦=−4
Pick a test point, say (0, 0)
3 0 −2(0)≥8
0≥8
𝑭𝒂𝒍𝒔𝒆
Shade away from the side that contains (0, 0) 9

10. Graphing Horizontal Line Inequality Ex: y > -2

11. Graphing Vertical Line Inequality Ex: x > -2

12. Graph the inequality in a coordinate plane.
Checkpoint
Graph Linear Inequalities in One Variable
Graph the inequality in a coordinate plane. 9. x
> 1 –
ANSWER
10. y ≥ 1
ANSWER

13. Graph the inequality in a coordinate plane.
Checkpoint
Graph Linear Inequalities in One Variable
Graph the inequality in a coordinate plane.
11. y ≤ 3 –
ANSWER
12.
< x 4
ANSWER

14. Homework WS 4.2