1. Graphing Linear Inequalities
Finite 3-1

2. How to Determine the Type of Line to Draw
Inequality Symbol
Type of Line
> or <
Dashed Line
Solid Line
More ink = more ink, less ink = less ink
How to Determine the Type of Line to Draw

3. 1. y > 3x - 2 a. Solid b. Dotted 2. y > ¼x - 5
Choose the type of line for the inequality given.

4. Choose the inequality symbol for the line shown.

5. Choose the inequality symbol for the line shown.

6. Shading If the inequality is: Shade y > mx + b or Above the line
Below the line
Shading

7. Graph y > x - 2. 1. Graph the line y = x - 2. x
2. Since y >, shade above the line. y

8. Graph y < x - 2. 1. Graph the line y = x - 2. x
2. Since y <, shade below the line. y

9. Do you do anything different when the line is dotted rather than solid?

10. Not Really

11. Graph y > x - 2. 1. Graph the line
y = x - 2, but make the line dotted. x
2. Since y >, shade above the line. y

12. Graph y < x - 2. 1. Graph the line
y = x - 2, but make the line dotted. x
2. Since y <, shade below the line. y

13. Graph y > -½x + 3 x y
Practice

14. Graph y > -½x + 3 x y

15. Choose the correct inequality for the graph shown.
y < 3 x + 2
y < 3 x + 2 x
y > 3 x + 2
y > 3 x + 2 y

16. Where to Shade for Undefined or No Slopes:
The inequality must be in
x  # (no y)
format.
 can be:
>, >, <, or <.

17. If the inequality is:
Shade
To the
x > # or
Right of the line
x < #
Left of the line

18. Graph x > -2 1. Draw a dotted vertical line at x = -2. x
2. Shade to the right of the line. y

19. Graph x < -2. 1. Graph the line X = -2. x
2. Shade to the left of the line. y

20. Graph x > 3. x y
Practice

21. Graph x > 3. x y
Practice

22. Solve -3x - 2y < 12.

23. Solve -3x - 2y < 12.
+3x +3x
-2y < 3x + 12
y < -3/2 x - 6
>

24. Choose the correct inequality. 1. 2x + 5y > -10

25. Example Which ordered pair is a solution of 5x - 2y ≤ 6? (0, -3)
(5, 5)
(1, -2)
(3, 3)
ANSWER: A. (0, -3)
Example

26. Graph the inequality x ≤ 4 in a coordinate plane.5 -5
Example

27. Example Graph the inequality x ≤ 4 in a coordinate plane.
Decide whether to
use a solid or
dashed line.
Use (0, 0) as a
test point.
Shade where the
solutions will be. y x 5 -5
Example

28. Graph 3x - 4y > 12 in a coordinate plane.5 -5
Example

29. Example Graph 3x - 4y > 12 in a coordinate plane.
Sketch the boundary line of the graph.
Solve for “y” first:
y < ¾x - 3
Solid or dashed
line?
Use (0, 0) as a
test point.
Shade where the
solutions are. y x 5 -5
Example

30. Graph y < 2/5x in a coordinate plane.-5
Example

31. Example Graph y < 2/5x in a coordinate plane.
What is the slope and y-intercept?
m = 2/5
b = (0,0)
Solid or dashed
line?
Use a test point
OTHER than the
origin.
Shade where the
solutions are. y x 5 -5
Example

32. Steps for Graphing a System of Inequalities
Graph each inequality and indicate which part should be shaded.
Shade the area which is common to all graphs or the area where the shading overlaps.
Pick any point in the commonly shaded area and check it in all inequalities.
Steps for Graphing a System of Inequalities

33. Systems Example: a: 3x + 4y > - 4 b: x + 2y < 2
Put in Slope-Intercept Form:
Systems

34. a: 3x + 4y > - 4
Systems

35. a: 3x + 4y > - 4
b: x + 2y < 2
Systems

36. a: 3x + 4y > - 4
b: x + 2y < 2
The area between the green arrows is the region of overlap and thus the solution.
Systems

37. Graph the following linear systems of inequalities.
Practice

38. x y
Use the slope and y-intercept to plot two points for the first inequality.
Draw in the line.
Shade in the appropriate region.
Practice

39. x y
Use the slope and y-intercept to plot two points for the second inequality.
Draw in the line.
Shade in the appropriate region.
Practice

40. x y
The final solution is the region where the two shaded areas overlap (purple region).
Practice

41. Graph the solution set of the system.
Practice

42. Practice Graph the solution set of the system.
First, we graph x + y  3 using a solid line.
Choose a test point (0, 0) and shade the correct plane.
Next, we graph x  y > 1 using a dashed line.
Choose a test point and shade the correct plane.
The solution set of the system of equations is the region shaded both red and green, including part of the line x + y  3.
Practice

43. What about THREE inequalities?
Graph x ≥ 0, y ≥ 0, and 4x + 3y ≤ 24
What about THREE inequalities?

44. What about THREE inequalities?
Graph x ≥ 0, y ≥ 0, and 4x + 3y ≤ 24
First off, let’s look at x ≥ 0 and y ≥ 0 separately.
What about THREE inequalities?

45. What about THREE inequalities?
Now let’s look at x ≥ 0 and y ≥ 0 together.
Clearly, the solution set is the first quadrant.
What about THREE inequalities?

46. What about THREE inequalities?
So therefore, after we graph the third inequality, we know the solution region will be trapped inside the first quadrant. So let’s look at 4x + 3y ≤ 24 by itself.
What about THREE inequalities?

47. What about THREE inequalities?
Now we can put all of our knowledge together.
The solution region is the right triangle in the first quadrant.
What about THREE inequalities?

48. Pages 118 – 120
9, 23, 25, 43a,b
Homework