See how to graph inequalities that include two variables.

1. Graphing Linear Inequalities
in Two Variables
Objectives:
Graph a linear inequality in two variables.
Model a real life situation using a linear inequality.

2. NOTE:
 If the sign is > 𝑜𝑟 <, the line is dashed.
 If the sign is ≥ 𝑜𝑟 ≤, the line is solid.
 When doing an inequality for just 𝑥.
 If the sign is >, shade to the right.
 If the sign is <, shade to the left.
 When doing an inequality for just 𝑦.
 If the sign is >, shade above.
 If the sign is <, shade below.

3. Example: Graph the inequality 𝑦 > 3 on the coordinate plane.

4. Example: Graph the inequality 𝑥 ≤ −2 on the coordinate plane.

5. NOTE:
 When dealing with lines that include both
variables, 𝑥 𝑎𝑛𝑑 𝑦.
 When it is > 𝑜𝑟 ≥, shade above the line.
 When it is < 𝑜𝑟 ≤, shade below the line.

6. EXAMPLES

7. Graph 𝑦 ≥ −3𝑥 + 2 on the coordinate plane.
Boundary line: 𝑦 = −3𝑥 + 2
The gradient, 𝑚 = −3.
The y-intercept, 𝑐 = 2.

8. NOTE: For a line of the form 𝑦 = 𝑚𝑥 + 𝑐

9. Graph 3𝑥 − 4𝑦 > 12 on the coordinate plane.
Step 1: Rewrite in the form 𝑦 = 𝑚𝑥 + 𝑐.
3𝑥 − 4𝑦 > 12
−4𝑦 > 12 − 3𝑥
𝑦 <
12 − 3𝑥
−4
𝑦 < −3 +
3
4
𝑥
This is the same as 𝒚 <
𝟑
𝟒
𝒙 − 𝟑.
Boundary line: 𝑦 =
3
4
𝑥 − 3.
The gradient, , 𝑚 =
3
4
.
The y-intercept, 𝑐 = −3.

10. PROBLEM
If you have less than $5.00 in five-cent
and ten-cent coins, write an inequality
to represent this information.
Then draw a graph to describe how
many of each type of coin you have.
Let 𝑛- number of five-cent coins.
Let 𝑑- number of ten-cent coins.
0.05𝑛 + 0.10𝑑 < 5.00
Rewrite as:
𝟓𝒏 + 𝟏𝟎𝒅 < 𝟓𝟎𝟎

11. Remember: To sketch the graph of a linear inequality:
• Solid Line
• Line a small shaded circle on the number line, a solid
line indicates that the boundary is included in the
solution set.
• Dashed Line
• Like a small unshaded circle on the number line, a
dashed line on the coordinate plane indicates that the
boundary is NOT a part of the solution set.