1. Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0
3. Write –6x + 2y = –4
in slope-intercept form,
and graph.
y = 3x – 2

2. Learning Target
Students will be able to: Graph and solve linear inequalities in two variables.

3. Tell whether the ordered pair is a solution of the inequality.
(–2, 4); y < 2x + 1
y < 2x + 1
4 2(–2) + 1
4 –4 + 1
4 –3
< 
(–2, 4) is not a solution.

4. (3, 1) is a solution.  (3, 1); y > x – 4 y > x − 4 1 3 – 4
– 4
1 – 1
> 
(3, 1) is a solution.

5.   a. (4, 5); y < x + 1 b. (1, 1); y > x – 7 y < x + 1
<
– 7
>
1 –6  
(4, 5) is not a solution.
(1, 1) is a solution.

6. A linear inequality describes a region of a coordinate plane called a half-plane. All points in the region are solutions of the linear inequality. The boundary line of the region is the graph of the related equation.

8. 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.

9.  Graph the solutions of the linear inequality. y  2x – 3
Check y  2x – 3
(0) – 3
0 –3  

10. The point (0, 0) is a good test point to use if it does not lie on the boundary line.
Helpful Hint

11.  Graph the solutions of the linear inequality. 5x + 2y > –8 Check
(0) – 4
0 –4
> 

12. Graph the solutions of the linear inequality.
2x – y – 4 > 0
Check

13.  Graph the solutions of the linear inequality. Check y ≥ x + 1
(0) + 1
0 ≥ 1 

14. Ada has at most 285 beads to make jewelry
Ada has at most 285 beads to make jewelry. A necklace requires 40 beads, and a bracelet requires 15 beads.
Write a linear inequality to describe the situation.
Let x represent the number of necklaces and y the number of bracelets.

15. Solve for y and graph. # of bracelets Remember, Ada can only use
whole numbers for x and y.
In Algebra 2 we will determine
which of those points
maximizes profit!
# of necklaces

16. Write an inequality to represent the graph.

17. Write an inequality to represent the graph.