Linear Inequalities in One and Two Variables

Transcription

1 Date:10/18/2014 Topic IV: Graphing Linear Inequalities in Two Variables 4 th Class Objective: the students will Graphing Linear Inequalities in Two Variables Real-World Applications Agenda: Bell ringer vocabulary: Examples : Topic 4 Resources Class work: Topic 4 Resources Closing Activity : Exit Ticket Homework:

2 Example 1 Check whether the given ordered pairs are solutions of the inequality. a) x 1; 1, 2, 5,

3 Example 1 Check whether the given ordered pairs are solutions of the inequality. b) y 5; 2, 6, 0,

4 Try these Check whether the given ordered pairs are solutions of the inequality. 4, 5, 2,1 1. y x 1;

5 Try these Check whether the given ordered pairs are solutions of the inequality. 3, 2, 2, x 9;

6 Example 2 Graph the inequality in the coordinate plane. a. 2x x 2 Solid line Test 0,0 0 2

7 Example 2 Graph the inequality in the coordinate plane. b. y 2 y 2 Dotted line Test 0,0 0 2

8 Example 2 Graph the inequality in the coordinate plane. c. 3x x 3 Solid line Test 0,0 0 3

9 Example 3 Graph the inequality. a. y x 2 Solid line Test 0,0 0 2

10 Example 3 Graph the inequality. 1 b. y x 2 Dotted line 4 Test 0,0 0 4

11 Graph the inequality. c. y x 3 Example 3 y x 3 Solid line Test 0,0 0 3

12 Graph the inequality. 3. y 3x 1 Dotted line Try this Test 1, 1 1 4

13 Graph the inequality. Try this 4. y 3x 1 Solid line Test 0,0 0 1

14 Graph the inequality. Try this 5. y 2x 1 Solid line Test 0,0 0 1

15 Example 4 Real word problems a. A concert charges $30 admission and $15 per shirt. Alyssa paid $75 at the concert for her admission and shirts. Write and solve an equation to find the number of shirts Alyssa bought. Explain what your variable represents. A. Let x = number of admission tickets; 30x + 15 =75; 2 tickets. B. Let x = number of admission tickets; 15x + 30 =75; 3 tickets. C. Let x = number of shirts; 30x + 15= 75; 2 shirts. D. Let x = number of shirts; 15x + 30 =75; 3 shirts.

16 Example 4 Real word problems a. A concert charges $30 admission and $15 per shirt. Alyssa paid $75 at the concert for her admission and shirts. Write and solve an equation to find the number of shirts Alyssa bought. Explain what your variable represents. Let x = number of shirts 15x x x 3 Alyssa bought 3 shirts

17 Example 4 Real word problems b. You rake leaves in your neighborhood after school and earn $6.50 per yard you rake. How many yards do you need to rake to earn at least $52? What equation models this situation? A. at least 45 yards; y , y = number of yards raked B. at least 8 yards; 6.50y 52.00, y = number of yards raked C. at most 8 yards; 6.50y < 52.00, y = number of dollars earned D. at most 52 yards; 6.5y > 52.00, y = number of dollars earned

18 Example 4 Real word problems b. You rake leaves in your neighborhood after school and earn $6.50 per yard you rake. How many yards do you need to rake to earn at least $52? What equation models this situation? Let x = number of leaves you rake per yard 6.5y y 8 you need to rake about 8 yards

19 Try this Real word problems 6. Marilyn spent a total of $52.34 on two new outfits. She bought two shirts for $12.99, a pair of pants for $18.50, and a skirt. If the sales tax rate was 7.5%, how much did she pay for the skirt? 7. The owners of a pet store want to spend a maximum of $700 for at least 6 minutes of advertising. The cost to advertise on a local TV station is $120 per minute. The cost to advertise on a local radio station is $75 per minute. Which inequality best represents the cost of buying r radio minutes and t TV minutes?

20 Try this 6. Marilyn spent a total of $52.34 on two new outfits. She bought two shirts for $12.99, a pair of pants for $18.50, and a skirt. If the sales tax rate was 7.5%, how much did she pay for the skirt? Let s = skirt s s s s s 17.20

21 Try this 7. The owners of a pet store want to spend a maximum of $700 for at least 6 minutes of advertising. The cost to advertise on a local TV station is $120 per minute. The cost to advertise on a local radio station is $75 per minute. Which inequality best represents the cost of buying r radio minutes and t TV minutes? Let t = The cost to advertise on a local TV station Let r = The cost to advertise on a local radio station 120t 75r 700

22 Example 5 The map show the number of the tickets needed for a small or large rides at the fair. You do nor want to spend more than $ 15 on tickets. How many small or large rides can you ride?

23 Example 5 What is the graph of each inequality? 3x 5y 60 find the intercepts of x int solid line C A 60 3 the boundary line y int C B

24 Try this 7. Suppose that you decide to spend no more than $ 30 for tickets. What are the possible combinations of small and large rides that you can ride now? Use a graph to find your answer. 3x 5y solid line 120 find the intercepts of x y int int C B C A the boundary line 40 24

25 Try this x int y int

26 Now Class work 4 th class Practice time!

27 Class work 4 th Class Name: date:

28 Class work 4 th Class Name: date:

29 Class work 4 th Class Name: date:

30 Class work 4 th Class Name: date:

31 Class work 4 th Class Name: date:

32 Exit ticket 4 th Class Name: date:

33 Homework 4 th Class