1. 3-1 Ordered Pairs Problem of the Day 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

2. 3-1 Ordered Pairs Learn to write solutions of equations in two variables as ordered pairs.

3. 3-1 Ordered Pairs Vocabulary ordered pair

4. 3-1 Ordered Pairs 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.

5. 3-1 Ordered Pairs y = $20 + $10 x Dominic’s team: = + Alyssa’s team: y = $20 + ($10 14) ‏ y = $20 + ($10 12) ‏ total cost of jerseys $20$10# of jerseys y = $160 y = $140

6. 3-1 Ordered Pairs 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).

7. 3-1 Ordered Pairs Determine whether each ordered pair is a solution of y = 4x – 1. Additional Example 1A: Deciding Whether an Ordered Pair Is a Solution of an Equation (3, 11) ‏ y = 4x – 1 11 = 4(3) – 1 ? Substitute 3 for x and 11 for y. 11 = 11 (3, 11) is a solution. Simplify. The order in which a solution is written is important. Always write x first, then y. Helpful Hint

8. 3-1 Ordered Pairs (10, 3) ‏ y = 4x – 1 3 = 4(10) – 1 ? Substitute 10 for x and 3 for y. 3 ≠ 39  (10, 3) is not a solution. Determine whether each ordered pair is a solution of y = 4x – 1. Additional Example 1B: Deciding Whether an Ordered Pair Is a Solution of an Equation Simplify.

9. 3-1 Ordered Pairs Determine whether each ordered pair is a solution of y = 5x + 3. Check It Out: Example 1A (7, 38) ‏ y = 5x + 3 38 = 5(7) + 3 ? Substitute 7 for x and 38 for y. 38 = 38 ? (7, 38) is a solution.

10. 3-1 Ordered Pairs Determine whether each ordered pair is a solution of y = 5x + 3. Check It Out: Example 1B (9, 17) ‏ y = 5x + 3 17 = 5(9) + 3 ? Substitute 9 for x and 17 for y. 17 = 48 ?  (9, 17) is not a solution.

11. 3-1 Ordered Pairs Use the given values to make a table of solutions. Additional Example 2A: Creating a Table of Ordered Pair Solutions y = x + 3 for x = 1, 2, 3, 4 xx + 3y(x, y) ‏ 1 2 3 4 1 + 34(1, 4) ‏ 2 + 3 5(2, 5) ‏ 3 + 3 6(3, 6) ‏ 4 + 3 7(4, 7) ‏ A table of solutions can be set up vertically or horizontally. Helpful Hint

12. 3-1 Ordered Pairs Use the given values to make a table of solutions. Additional Example 2B: Creating a Table of Ordered Pair Solutions n = 6m – 5 for m = 1, 2, 3 6(1) – 56(2) – 56(3) – 5 1713 (1, 1) ‏ (2, 7) ‏ (3, 13) ‏ m123 6m – 5 n (m, n) ‏

13. 3-1 Ordered Pairs Use the given values to make a table of solutions. y = x + 6 for x = 1, 2, 3, 4 xx + 6y(x, y) ‏ 1 2 3 4 1 + 67(1, 7) ‏ 2 + 6 8 (2, 8) ‏ 3 + 6 9 (3, 9) ‏ 4 + 610(4, 10) ‏ Check It Out: Example 2A

14. 3-1 Ordered Pairs Use the given values to make a table of solutions. n = 8m – 2 for m = 1, 2, 3, 4 30 8(1) – 28(2) – 28(3) – 2 61422 (1, 6) ‏ (2, 14) ‏ (3, 22) ‏ (4, 30) ‏ 8(4) – 2 m123 8m – 2 n (m, n) ‏ 4 Check It Out: Example 2B

15. 3-1 Ordered Pairs 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. Additional Example 3A: Consumer Math Application What will be the sales price of a sweater with a wholesale cost of $48? p = 1.2(48) p = 57.6 The $48 wholesale sweater will cost the customer $57.60, so (48, 57.60) is a solution of the equation. The wholesale cost of the sweater before tax is $48. Multiply.

16. 3-1 Ordered Pairs Additional Example 3B: Consumer Math Application What will be the sales price of a jacket with a wholesale cost of $85? p = 1.2(85) p = 102 The $85.00 wholesale jacket will cost the customer $102, so (85, 102) is a solution of the equation. The wholesale cost of the jacket before tax is $85. Multiply. 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.

17. 3-1 Ordered Pairs 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. Check It Out: Example 3A How much will a $22 item cost after sales tax? c = 1.075(22) c = 23.65 After sales tax, the $22 item will cost $23.65, so (22, 23.65) is a solution to the equation. The price of the item before tax is $22. Multiply.

18. 3-1 Ordered Pairs 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. Check It Out: Example 3B How much will a $10 item cost after sales tax? c = 1.075(10) c = 10.75 After sales tax, the $10 item will cost $10.75, so (10, 10.75) is a solution to the equation. The price of the item before tax is $10. Multiply.

19. 3-1 Ordered Pairs Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. 3-1 Ordered Pairs Lesson Quiz: Part I Determine whether each ordered pair is a solution of y = 4x – 7. 1. (2, 15) 2. (4, 9) ‏ 3. Use the given values to make a table of solutions. y = 4x  6 for x = 2, 4, 6, 8, and 10 yesno (10, 34) ‏ 344(10) – 610 (8, 26) ‏ 264(8) – 68 (6, 18) ‏ 184(6) – 66 (4, 10) ‏ 104(4) – 64 (2, 2) ‏ 24(2) – 62 (x, y) ‏ y4x – 6x

21. 3-1 Ordered Pairs Lesson Quiz: Part II 4. A plumbing company charges $50 for a service call and $15 per hour. They went on a 3-hour job. How much did the company earn? c = 15n + 50; $95

22. 3-1 Ordered Pairs 1. Which of the following ordered pairs is the solution of y = 6x – 9? A. (1, 3) B. (2, 3) C. (3, 2) D. (3, 7) Lesson Quiz for Student Response Systems

23. 3-1 Ordered Pairs 2. Which of the following ordered pairs is NOT the solution of y = 4x + 7? A. (4, 23) B. (5, 20) C. (1, 11) D. (3, 19) Lesson Quiz for Student Response Systems

24. 3-1 Ordered Pairs 3. Use the given values to identify the table of solutions. y = 6x – 4 for x = 1, 3, 5, 7, and 9 A. B. Lesson Quiz for Student Response Systems

25. 3-1 Ordered Pairs 4. The water level in a tank is 17 feet. Due to the heavy rainfall, the water level increases at the rate of 7 feet per hour. What will be the water level in the tank after 5 hours? A. L = 17n + 17; 102 ft B. L = 17n + 7; 92 ft C. L = 7n + 17; 52 ft D. L = 7n + 7; 42 ft Lesson Quiz for Student Response Systems