1. 2.7 Two-Variable Inequalities
Graphing Linear Inequalities
Graphing Absolute-Value Inequalities

3. 1) Graphing Linear Inequalities
The graph of a linear inequality is a region of the coordinate plane that is bounded by a line

4. 1) Graphing Linear Inequalities
What it shows…
the values on the coordinate plane that apply to the function
What an equation looks like…

5. 1) Graphing Linear Inequalities
What it shows…
the values on the coordinate plane that apply to the function
What an equation looks like…
Inequality symbol
Slope
y-intercept

6. 1) Graphing Linear Inequalities
What linear inequality graphs look like…
1) boundary line
(solid or dashed)
2) shaded area
(above or below the boundary line)

7. 1) Graphing Linear Inequalities
A dashed boundary line means the line is NOT part of the solution
The shading is ABOVE the boundary line if the equation is of the form
y > OR y >
y < OR y >

8. 1) Graphing Linear Inequalities
A solid boundary line means the line IS part of the solution
The shading is BELOW the boundary line if the equation is of the form
y < OR y <
y < OR y >

9. 1) Graphing Linear Inequalities
Example 1:
Graph the inequality y < 2x + 2

10. 1) Graphing Linear Inequalities
Remember… y = mx + b
Example 1:
Graph the inequality y < 2x + 2

11. 1) Graphing Linear Inequalities
Remember… y = mx + b
Example 1:
Graph the inequality y < 2x + 2
y-int = 2
m = 2

12. 1) Graphing Linear Inequalities
Example 1:
Graph the inequality y < 2x + 2
y-int = 2
m = 2

13. 1) Graphing Linear Inequalities
Example 1:
Graph the inequality y < 2x + 2
y-int = 2
m = 2

14. 1) Graphing Linear Inequalities
Example 1:
Graph the inequality y < 2x + 2
y-int = 2
m = 2

15. 1) Graphing Linear Inequalities
Example 1:
Graph the inequality y < 2x + 2
y-int = 2
m = 2
y <
DASHED line

16. 1) Graphing Linear Inequalities
Example 1:
Graph the inequality y < 2x + 2
y-int = 2
m = 2
y <
SHADE BELOW the line

17. 1) Graphing Linear Inequalities
Example 2:
Write an inequality for the graph below.

18. 1) Graphing Linear Inequalities
Example 2:
Write an inequality for the graph below.
y = mx + b
y –int =
m =
inequality type

19. 1) Graphing Linear Inequalities
Example 2:
Write an inequality for the graph below.
y = mx + b
y –int =
m =
inequality type

20. 1) Graphing Linear Inequalities
Example 2:
Write an inequality for the graph below.
y = mx + b
y –int = -3
m =
inequality type

21. 1) Graphing Linear Inequalities
Example 2:
Write an inequality for the graph below.
y = mx + b
y –int = -3
m = -3/2
inequality type >

22. 1) Graphing Linear Inequalities
Example 2:
Write an inequality for the graph below.
y –int = -3
m = -3/2
inequality type >
Sub into y > mx + b

23. 1) Graphing Linear Inequalities
Example 2:
Write an inequality for the graph below.
y –int = -3
m = -3/2
inequality type >
Sub into y > mx + b
y > -3x/2- 3

24. Homework p.104 #1, 5, 7, 20, 21, 23, 26, 37, 38 Don’t forget…
Quiz TUESDAY
Test FRIDAY

25. 2) Absolute Value Inequalities
Graph the absolute value function then shade above OR below

26. 2) Absolute Value Inequalities
Graph the absolute value function then shade above OR below
Solid line…y <, y>
Dashed line…y<, y>
Shade above y>, y>
Shade below…y<, y<

27. 2) Absolute Value Inequalities
Example 1:
Graph y < |x – 2| + 3

28. 2) Absolute Value Inequalities
Example 1:
Graph y < |x – 2|
DASHED line
Shade BELOW
slope = 1
Vertex = (2, 3)

29. 2) Absolute Value Inequalities
Example 1:
Graph y < |x – 2|
slope = 1
DASHED line
Shade BELOW
Vertex = (2, 3)

30. 2) Absolute Value Inequalities
Example 1:
Graph y < |x – 2|
slope = 1
DASHED line
Shade BELOW
Vertex = (2, 3)

31. 2) Absolute Value Inequalities
Example 1:
Graph y < |x – 2|
slope = 1
DASHED line
Shade BELOW
Vertex = (2, 3)

32. 2) Absolute Value Inequalities
Example 1:
Graph y < |x – 2|
slope = 1
DASHED line
Shade BELOW
Vertex = (2, 3)

33. 2) Absolute Value Inequalities
Example 1:
Graph y < |x – 2|
slope = 1
DASHED line
Shade BELOW
Vertex = (2, 3)

34. 2) Absolute Value Inequalities
Example 2:
Graph –y + 1 < -2|x + 2|

35. 2) Absolute Value Inequalities
Example 2:
Graph –y + 1 < -2|x + 2|
-y < -2|x + 2| - 1
y > 2|x + 2| + 1
-y so CHANGE the direction of the inequality

36. 2) Absolute Value Inequalities
y > 2|x |

37. 2) Absolute Value Inequalities
y > 2|x |
Slope = 2
Solid line
Shade above
Vertex = (-2, 1)

38. 2) Absolute Value Inequalities
y > 2|x |

39. 2) Absolute Value Inequalities
y > 2|x |

40. 2) Absolute Value Inequalities
y > 2|x |

41. 2) Absolute Value Inequalities
y > 2|x |

42. 2) Absolute Value Inequalities
Example 3:
Write an equation for the graph below.

43. Homework p.104 #11-13, 22, 30, 39-42 Reminders…
Quiz TUESDAY (2.5, 2.6, first half 2.7)
Review WEDNESDAY, THURSDAY
Test FRIDAY (Chapter 2 ONLY)
Extra-help WEDNESDAY at LUNCH