1. Lesson Objective: I will be able to …
Graph and solve linear inequalities in two variables
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

2. Page 24
A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol.
A solution of a linear inequality is any ordered pair that makes the inequality true.

3. Example 1: Identifying Solutions of Inequalities
Page 26
Tell whether the ordered pair is a solution of the inequality.
(–2, 4); y < 2x + 1
y < 2x + 1
4 2(–2) + 1
Substitute (–2, 4) for (x, y).
4 –4 + 1
4 –3
< 
(–2, 4) is not a solution.

4. Your Turn 1
Page 26
Tell whether the ordered pair is a solution of the inequality.
(4, 5); y > x + 1
y > x + 1
>
Substitute (4, 5) for (x, y). 
(4, 5) is not a solution.

5. Page 25

6. Graphing Linear Inequalities
Page 25
Graphing Linear Inequalities
Step 1
Solve the inequality for y (slope-intercept form).
Step 2
Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.
Step 3
Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer.

7. Example 2: Graphing Linear Inequalities in Two Variables
Page 27
Graph the solutions of the linear inequality.
y  2x – 3
Step 1 The inequality is already solved for y.
Step 2 Graph the boundary line y = 2x – 3. Use a solid line for .
Step 3 The inequality is , so shade below the line.
Check y  2x – 3
(0) – 3
0 –3  
The point (0, 0) is a good test point to use if it does not lie on the boundary line.
Helpful Hint

8. Your Turn 2 Graph the solutions of the linear inequality:
Page 28
Graph the solutions of the linear inequality:
4x – 3y > 12
Step 2 Graph the boundary line y = – 4. Use a dashed line for <.
Step 1 Solve the inequality for y.
4x – 3y > 12
–4x –4x
–3y > –4x + 12
y < – 4
Check
y < – 4
– (1) – 4
– – 4
–6 < 

9. Example 3: Writing an Inequality from a Graph
Page 28
Write an inequality to represent the graph.
y-intercept: 1; slope:
Write an equation in slope-intercept form.
The graph is shaded above a dashed boundary line.
Replace = with > to write the inequality

10. Write an inequality to represent the graph.
Your Turn 3
Page 29
Write an inequality to represent the graph.
y-intercept: 0 slope: –1
Write an equation in slope-intercept form.
y = mx + b y = –1x
The graph is shaded below a dashed boundary line.
Replace = with < to write the inequality y < –x.

11. Homework
Assignment #35
Holt 6-5 #12, 13, 15, 19-21, 23, 26, 63