1. Bellwork
Determine whether the ordered pairs are solutions of the inequality: 2x-3y>-2
1.) (0,0)
2.) (0,1)

2. 2x-3y>-2 2(0) - 3(0) > -2 0 - 0 > -2 0 > -2
1.) (0,0) is the ordered Pair
2(0) - 3(0) > -2
0 - 0 > -2
0 > -2
True

3. 2x-3y>-2 2(0) - 3(1) > -2 0 - 3 > -2 -3 > -2
1.) (0,1) is the ordered Pair
2(0) - 3(1) > -2
0 - 3 > -2
-3 > -2
False

4. To be able to graph a linear inequality in two variables.
Today’s Objective
To be able to graph a linear inequality in two variables.

5. Graphing a linear equation in slope-intercept form.
Recall
Graphing a linear equation in slope-intercept form.
y = mx + b

6. Finding the slope and y-intercept
Find the Slope and y-intercept of the following equation.
y = 3x + 2

7. Finding the slope and y-intercept
When the equation is in the form y = mx + b The slope is m, and the y-intercept is b, So…...

8. y = mx + b For the equation y = 3x + 2 The Slope is 3
The y-intercept is 2

9. Graphing equations in the form y = mx + b
Graph the equation y = 3x+ 2
The y-intercept is 2
The slope is 3 which means the rise is 3 and the run is 1.
So….

10. y = 3x + 2 Y
Slope = 3
y-intercept= 2 X
Up 3 and over 1

11. You Try this one y = -2x + 3 Down 2 and over 1 Slope = -2
y-intercept= 3 X
Down 2 and over 1

12. Now pick a point on one side of the dotted line (0,0)
Graph x < -3 & y < 4
Sketch x = -3 and y = 4 Y
x = -3
Now pick a point on one side of the dotted line (0,0) X

13. x < -3 0 < -3 Test a Point
Take the point (0,0) and plug in the x value in x < -3
x < -3
0 < -3
False
since it’s false, shade the side opposite of (0,0)….

14. Graph x < -3 & y < 4 x = -3
Shade the true side & every point on this side solves the inequality. Y
x = -3 X
(0,0)

15. Now pick a point on one side of the solid line (0,0)
Graph x < -3 & y < 4
Sketch x = -3 and y = 4 Y
y = 4
Now pick a point on one side of the solid line (0,0) X

16. Test a Point
Take the point (0,0) and plug in the y value in y < 4
y < 4
0 < 4
True
since it’s True, shade the side that (0,0) is on….

17. Graph x < -3 & y < 4 Y
Shade the True Side & every point on this side solves the inequality.
y = 4 X
(0,0)

18. What’s the difference between the dotted line and the solid line?
Graph x < -3 & y < 4 Y
y < 4 X
x < -3
What’s the difference between the dotted line and the solid line?

19. Now pick a point on one side of the dotted line (0,0)
Graph x + y > 3
Sketch y = -x + 3 Y
y= -x +3
Now pick a point on one side of the dotted line (0,0) X

20. since it’s True, shade the side that (0,0) is on….
Test a Point
Take the point (0,0) and plug in the values in y < -x + 3
y < -x + 3
0 <
0 < 3
True
since it’s True, shade the side that (0,0) is on….

21. Graph x + y > 3 Y
y= -x +3 X
(0,0)

22. You try this one
Graph y < 2x - 1

23. Now pick a point on one side of the dotted line -(-1,0)
Graph y < 2x - 1
Sketch y = 2x - 1 Y
y= 2x - 1
Now pick a point on one side of the dotted line -(-1,0) X

24. since it’s False, shade the opposite side of (-1,0). on….
Test a Point
Take the point (-1,0) and plug in the values in y < 2x - 1
y < 2x - 1
0 < 2(-1) -1
0 < -3
False
since it’s False, shade the opposite side of (-1,0). on….

25. Graph y > 2x - 1 Y
y= 2x - 1 X
(-1,0)

26. Classwork
Do worksheet 6.5
Homework page 323 (7 - 26)

27. Page 323 (7-26) 7.) (1,3) 8.) Neither 9.) Both 10.) Neither 11.) -2 22 4 6

28. Page 323 (7 - 26)
12.)
13.)
14.) -2 2 4 6 -2 2 4 6 -2 2 4 6

29. Page 323 (7-26)
15.) C
16.) B
17.) D
18.) A

30. 19.) Graph -x - y < 4 Y X
(0,0)

31. 20.) Graph 2x - y > 6 Y X
(0,0)

32. 21.) Graph 3x + y > 9 Y X
(0,0)

33. 22.) Graph y - 4x < 0 Y X
(0,0)

34. Page 323 (7 -26) 23.) y < -2x + 2 24.) y > 2/5x - 2