1. Graphing a Linear Inequality
So far, we have been graphing linear equality lines (i.e. y = 2x + 1)
Now let’s look at graphing linear inequality lines (i.e. y > 2x + 1)
Graphing a linear inequality is very similar to graphing a linear equality.

2. Graphing a Linear Inequality
Step 1) Solve the inequality for y (or for x if there is no y).
Step 2) Change the inequality to an equation and graph like before
Step 3) If the inequality is < or > (not equals), the line is dashed ( ).
If the inequality is ≤ or ≥, the line is solid (______).
Step 4) If the inequality is < or ≤, you shade below or to the left of the line.
If the inequality is > or ≥, you shade above or to the right of the line.

3. Graph: y- 2x ≤ + 1 Step 1: Solve the inequality for y: y ≤ 2x+1
Step 2: Graph the line y = 2x + 1
Step 3: Because y ≤ 2x+1 and not <, the line
will be solid
Step 4: Now shade the side of the line where
y < 2x+1 (below the line).

4. Graph -y – x < 2 Step 1: Solve the inequality for y: y > -x – 2
Step 2: Graph the equality y = -x – 2
Step 3: Because y > -x – 2 and not ≥, the line
will be dotted
Step 4: Now shade the side of the line where
y > -x - 2 (above the line).

5. Graph the inequality 3 – x > 0
Step 1: Solve the inequality for x
3 - x > 0
-x > -3
x < 3

6. Graph: x < 3 Step 2: Graph the line x = 3 Step 3: Because x < 3,
the line will be dotted
Step 4: Now shade the side
of the line where
x < 3 (to the left of
the line) 6 4 2 3

7. Check if your graph is correct
To check that the shading is correct, pick a point in the area and plug it into the inequality.
If the inequality statement is true, the shading is correct. If the inequality statement is false, the shading is incorrect.

8. Check if your graph is correct
Pick a point, (1,2),
in the shaded area.
Substitute into the
original inequality
3 – x > 0
3 – 1 > 0
2 > 0
True! The inequality
has been graphed
correctly. 6 4 2 3

9. Given the inequality graphed below:
a.) Write an inequality statement.
b.) Name one ordered pair that is not in the solution set.
c.) Name one ordered pair that is in the solution set.

10. Given the inequality graphed below:
a.) Write an inequality statement.
b.) Name one ordered pair that is not in the solution set.
c.) Name one ordered pair that is in the solution set.

11. Write a system of inequalities for the dark blue solution shown on the graph below.
(Hint: you should write 2 different inequalities – one for each graph)

12. Write a system of inequalities for the green solution shown on the graph below.
(Hint: you should write 2 different inequalities – one for each graph)

13. Write a system of inequalities for the dark blue solution shown on the graph below.
(Hint: you should write 2 different inequalities – one for each graph)

14. Write a system of inequalities for the dark blue solution shown on the graph below.
(Hint: you should write 2 different inequalities – one for each graph)

15. Write a system of inequalities for the blue solution shown on the graph below.
(Hint: you should write 3 different inequalities – one for each graph)