1. 3.5 Graphing Linear
Inequalities in Two
Variables

2. What is a Linear Inequality?
• An inequality containing x and y
whose boundary is a straight line.

3. Checking Solutions
• Solutions of linear inequalities are
ordered pairs (x, y) that make the
inequality true.
• To check if a point is a solution:
▫ Plug it in for x and y
▫ Simplify
▫ Does it make a true statement?

4. Example
• Is (-1, 9) a solution of 2x + y < -3 ?

5. Example
• Is (2, -2) a solution of x – 3y ≥ 8 ?

6. Example
• Is (-3, 4) a solution of y > -1 ?

7. Example
• Is (0, 0) a solution of y > x ?

8. You Try!
• Is (-4, -1) a solution of 5x – 2y ≤ -1?

9. Graphs of Linear
Inequalities
• Linear inequalities, like linear
equations, cannot be “solved” to get a
number answer.
• Instead, we use a graph to show all
solutions!
• Graphs will contain a “boundary
line” and a shaded “half plane.”

10. Dashed or Solid
• A dashed line means points on
the line are not solutions.
▫ Use for < and >.
• A solid line means points on the
line are solutions.
▫ Use for ≤ and ≥.

11. Where to Shade?
• The shaded area shows all possible
points that make the inequality true.
• Test a point.
▫ We usually use (0,0).
▫ If it is on the line, choose a different
point.
• If it is a solution, shade that side.
• If it is not a solution, shade the other
side.

12. Graphing Simple Linear
Inequalities
• Linear inequalities with only one
variable have horizontal or vertical
boundary lines.
• x: vertical (up and down)
• y: horizontal (side to side)

13. Example:
• Graph y ≤ 2.

14. Example:
• Graph x > 1.

15. Example:
• Graph y ≥ -5.

16. You Try!
Graph y > -1
Graph 3.5 > x

17. Slope-Intercept Form
• Remember: y = mx + b
• m = slope
▫ rise over run!
• (0, b) = y-intercept

18. Example
• Graph y ≤ 3x – 1

19. Example
• Graph y > ½ x + 3

20. Example
• Graph y ≥ - x – 2

21. You Try!
• Graph y < x + 2

22. Standard Form
• Remember: ax + by = c
• Two choices:
▫ Solve for y. Rewrite as y = mx + b.
- or ▫ Find intercepts: (0, y) and (x, 0)

23. Graphing Practice/Review
• Graph 3x + 2y = -6 both ways.

24. Example
• Graph –x + 2y > 2

25. Example
• Graph 3x – 2y < 6

26. Example
• Graph 3x – 2y ≥ 0

27. You Try!
• Graph –x + 4y > – 2