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:
Example 1 Check whether the given ordered pairs are solutions of the inequality. a) x 1; 1, 2, 5, 2 1 1 5 1
Example 1 Check whether the given ordered pairs are solutions of the inequality. b) y 5; 2, 6, 0, 2 6 5 2 5
Try these Check whether the given ordered pairs are solutions of the inequality. 4, 5, 2,1 1. y x 1; 5 4 1 5 5 1 2 1 1 1
Try these Check whether the given ordered pairs are solutions of the inequality. 3, 2, 2, 5 2. 4x 9; 43 9 12 9 4 2 9 8 9
Example 2 Graph the inequality in the coordinate plane. a. 2x 4 2 2 x 2 Solid line Test 0,0 0 2
Example 2 Graph the inequality in the coordinate plane. b. y 2 y 2 Dotted line Test 0,0 0 2
Example 2 Graph the inequality in the coordinate plane. c. 3x 9 3 3 x 3 Solid line Test 0,0 0 3
Example 3 Graph the inequality. a. y x 2 Solid line Test 0,0 0 2
Example 3 Graph the inequality. 1 b. y x 2 Dotted line 4 Test 0,0 0 4
Graph the inequality. c. y x 3 Example 3 y x 3 Solid line Test 0,0 0 3
Graph the inequality. 3. y 3x 1 Dotted line Try this Test 1, 1 1 4
Graph the inequality. Try this 4. y 3x 1 Solid line Test 0,0 0 1
Graph the inequality. Try this 5. y 2x 1 Solid line Test 0,0 0 1
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.
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 30 75 30-30 15x 45 15 15 x 3 Alyssa bought 3 shirts
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 + 6.5 52.00, 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
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 52 6.5 6.5 y 8 you need to rake about 8 yards
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?
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.99 18.501.075 12 s 1.075 52.34.491.075 31 s 1.075 s 33.85 s 1.075 52.34 52.34 1.075 18.49 s 17.20
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
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?
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 20 12 y int C B 60 5 12 20
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 120 3 120 5 the boundary line 40 24
Try this x int y int
Now Class work 4 th class Practice time!
Class work 4 th Class Name: date:
Class work 4 th Class Name: date:
Class work 4 th Class Name: date:
Class work 4 th Class Name: date:
Class work 4 th Class Name: date:
Exit ticket 4 th Class Name: date:
Homework 4 th Class