Graphing Inequalities in the Coordinate Plane

1. Section 5-7
Graphing Inequalities in the Coordinate Plane

2. Warm-up
Graph the following.
1. x ≤ 3 2. t > -4
3. y = 2x - 1

3. Warm-up
Graph the following.
1. x ≤ 3 2. t > -4
x
-2 -1 0 1 2 3 4
3. y = 2x - 1

4. Warm-up
Graph the following.
1. x ≤ 3 2. t > -4
x t
-2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1
3. y = 2x - 1

5. Warm-up
Graph the following.
1. x ≤ 3 2. t > -4
x t
-2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1
3. y = 2x - 1
y
x

8. Half-plane:

9. Half-plane: A region formed on a plane when a line is
placed on it

10. Half-plane: A region formed on a plane when a line is
placed on it
Boundary:

11. Half-plane: A region formed on a plane when a line is
placed on it
Boundary: The line that divides the plane in half

12. Example 1
Graph y < 3 on a coordinate plane.

13. Example 1
Graph y < 3 on a coordinate plane.

14. Example 1
Graph y < 3 on a coordinate plane.
(This is the INEQUALZ app on the TI-84)

15. Graphing Linear Inequalities

16. Graphing Linear Inequalities
1. Treat inequalities as if the were equations, yet be mindful of
the signs

17. Graphing Linear Inequalities
1. Treat inequalities as if the were equations, yet be mindful of
the signs
2. Graph the boundary line
*Dashed for <, >, ≠
*Solid for ≤, ≥

18. Graphing Linear Inequalities
1. Treat inequalities as if the were equations, yet be mindful of
the signs
2. Graph the boundary line
*Dashed for <, >, ≠
*Solid for ≤, ≥
3. Shade appropriately
*Check points
*When in “slope-intercept” form, the sign will tell you to
shade above or below the boundary line

19. Example 2
Graph y ≥ 4/3 x + 5

20. Example 2
Graph y ≥ 4/3 x + 5

21. Lattice Points

22. Lattice Points
Points whose coordinates are integers

23. Example 3
Matt Mitarnowski has at most $1.50 in his pocket.
a. Draw a graph showing all possible combinations of
dimes and quarters Matt could have.

24. Example 3
Matt Mitarnowski has at most $1.50 in his pocket.
a. Draw a graph showing all possible combinations of
dimes and quarters Matt could have.
15.0
12.5
10.0
Dimes
7.5
5.0
2.5
0
0 1 2 3 4 5 6
Quarters

25. Example 3
b. How many coordinates are there?

26. Example 3
b. How many coordinates are there?
58 total possible combinations of quarters and dimes

27. Homework

28. Homework
p. 316 #1 - 26
“To have a right to do a thing is not at all the same
as to be right in doing it.” - GK Chesterton