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# AA Section 5-7

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Graphing Inequalities in the Coordinate Plane

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### AA Section 5-7

1. 1. Section 5-7 Graphing Inequalities in the Coordinate Plane
2. 2. Warm-up Graph the following. 1. x ≤ 3 2. t > -4 3. y = 2x - 1
3. 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. 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. 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
6. 6. Half-plane:
7. 7. Half-plane: A region formed on a plane when a line is placed on it
8. 8. Half-plane: A region formed on a plane when a line is placed on it Boundary:
9. 9. Half-plane: A region formed on a plane when a line is placed on it Boundary: The line that divides the plane in half
10. 10. Example 1 Graph y < 3 on a coordinate plane.
11. 11. Example 1 Graph y < 3 on a coordinate plane.
12. 12. Example 1 Graph y < 3 on a coordinate plane. (This is the INEQUALZ app on the TI-84)
13. 13. Graphing Linear Inequalities
14. 14. Graphing Linear Inequalities 1. Treat inequalities as if the were equations, yet be mindful of the signs
15. 15. 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 ≤, ≥
16. 16. 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
17. 17. Example 2 Graph y ≥ 4/3 x + 5
18. 18. Example 2 Graph y ≥ 4/3 x + 5
19. 19. Lattice Points
20. 20. Lattice Points Points whose coordinates are integers
21. 21. 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.
22. 22. 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
23. 23. Example 3 b. How many coordinates are there?
24. 24. Example 3 b. How many coordinates are there? 58 total possible combinations of quarters and dimes
25. 25. Homework
26. 26. 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