2-1 Ordered Pairs. Lesson Presentation

Transcription

1 Lesson Presentation

2 Practice Problems Solve. A. x 8 = 19 B. 5 = a 2 C. 7 + n = 24 D. 3c 7 = 32 E. 17y + 7 = 58 x = 27 a = 7 n = 17 c = 13 y = 3

3 Practice Problem F A moving van travels 50 miles per hour. Use the equation y = 50x, where x represents the number of hours. How far will the van travel in 4.5 hours? 225 miles

4 Learn to write solutions of equations in two variables as ordered pairs.

5 ordered pair Vocabulary

6 The company that makes team uniforms for a soccer league charges a $20 fee for team artwork and $10 for each jersey. Dominic s team has 14 players, and Alyssa s team has 12 players. Find the cost for a set of jerseys for each team. Let y be the total cost of a set of jerseys and x be the number of jerseys needed.

7 total cost of jerseys = $20 + $10 # of jerseys y = $20 + $10 x Dominic s team: y = $20 + ($10 14) y = $160 Alyssa s team: y = $20 + ($10 12) y = $140

8 An ordered pair (x, y) is a pair of numbers that can be used to locate a point on a coordinate plane. A solution of a two-variable equation can be written as an ordered pair. The ordered pair (14, 160) is a solution because 160 = $20 + ($10 14). The ordered pair (12, 140) is a solution because 140 = $20 + ($10 12).

9 Additional Example 1A: Deciding Whether an Ordered Pair Is a Solution of an Equation Determine whether each ordered pair is a solution of y = 4x 1. (3, 11) y = 4x 1? 11 = 4(3) 1 11 = 11 (3, 11) is a solution. Substitute 3 for x and 11 for y. Simplify. Helpful Hint The order in which a solution is written is important. Always write x first, then y.

10 Additional Example 1B: Deciding Whether an Ordered Pair Is a Solution of an Equation Determine whether each ordered pair is a solution of y = 4x 1. (10, 3) y = 4x 1? 3 = 4(10) (10, 3) is not a solution. Substitute 10 for x and 3 for y. Simplify.

11 Check It Out: Example 1A Determine whether each ordered pair is a solution of y = 5x + 3. (7, 38) y = 5x + 3? 38 = 5(7) + 3? 38 = 38 (7, 38) is a solution. Substitute 7 for x and 38 for y.

12 Check It Out: Example 1B Determine whether each ordered pair is a solution of y = 5x + 3. (9, 17) y = 5x + 3? 17 = 5(9) + 3? 17 = 48 (9, 17) is not a solution. Substitute 9 for x and 17 for y.

13 Additional Example 2A: Creating a Table of Ordered Pair Solutions Use the given values to make a table of solutions. y = x + 3 for x = 1, 2, 3, 4 x x + 3 y (x, y) (1, 4) (2, 5) (3, 6) (4, 7) Helpful Hint A table of solutions can be set up vertically or horizontally.

14 Additional Example 2B: Creating a Table of Ordered Pair Solutions Use the given values to make a table of solutions. n = 6m 5 for m = 1, 2, 3 m m 5 n (m, n) 6(1) 5 6(2) 5 6(3) (1, 1) (2, 7) (3, 13)

15 Check It Out: Example 2A Use the given values to make a table of solutions. y = x + 6 for x = 1, 2, 3, 4 x x + 6 y (x, y) (1, 7) (2, 8) (3, 9) (4, 10)

16 Check It Out: Example 2B Use the given values to make a table of solutions. n = 8m 2 for m = 1, 2, 3, 4 m m 2 8(1) 2 8(2) 2 8(3) 2 8(4) 2 n (m, n) (1, 6) (2, 14) (3, 22) (4, 30)

17 Additional Example 3A: Consumer Math Application A salesman marks up the price of everything he sells by 20%. The equation for the sales price p is p = 1.2w, where w is wholesale cost. What will be the sales price of a sweater with a wholesale cost of $48? p = 1.2(48) p = 57.6 The wholesale cost of the sweater before tax is $48. Multiply. The $48 wholesale sweater will cost the customer $57.60, so (48, 57.60) is a solution of the equation.

18 Additional Example 3B: Consumer Math Application A salesman marks up the price of everything he sells by 20%. The equation for the sales price p is p = 1.2w, where w is wholesale cost. What will be the sales price of a jacket with a wholesale cost of $85? p = 1.2(85) p = 102 The wholesale cost of the jacket before tax is $85. Multiply. The $85.00 wholesale jacket will cost the customer $102, so (85, 102) is a solution of the equation.

19 Check It Out: Example 3A In most states, the price of each item is not the total cost. Sales tax must be added. If sales tax is 7.5%, the equation for total cost is c = 1.075p, where p is the price before tax. How much will a $22 item cost after sales tax? c = 1.075(22) c = The price of the item before tax is $22. Multiply. After sales tax, the $22 item will cost $23.65, so (22, 23.65) is a solution to the equation.

20 Check It Out: Example 3B In most states, the price of each item is not the total cost. Sales tax must be added. If sales tax is 7.5%, the equation for total cost is c = 1.075p, where p is the price before tax. How much will a $10 item cost after sales tax? c = 1.075(10) c = The price of the item before tax is $10. Multiply. After sales tax, the $10 item will cost $10.75, so (10, 10.75) is a solution to the equation.

21 Assignments: 1.) Ch. 2-1 Review Packet Mon ) Pg. 52 (1-24) Tues ) 3 graphing sheets Wed