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2-1 Ordered Pairs Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 2-1 Ordered Pairs Warm Up Solve. 1. x – 8 = 19 2. 5 = a – 2 x = 27 a=7 3. 7 + n = 24 n = 17 4. 3c – 7 = 32 c = 13 5. 17y + 7 = 58 y=3 2-1 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 2-1 Ordered Pairs Learn to write solutions of equations in two variables as ordered pairs. 2-1 Ordered Pairs Vocabulary ordered pair 2-1 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. 2-1 Ordered Pairs 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 2-1 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). 2-1 Ordered Pairs 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 Substitute 3 for x and 11 for y. 11 = 11 Simplify. (3, 11) is a solution. Helpful Hint The order in which a solution is written is important. Always write x first, then y. 2-1 Ordered Pairs 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) – 1 Substitute 10 for x and 3 for y. Simplify. 3 ≠ 39 (10, 3) is not a solution. 2-1 Ordered Pairs 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 ? Substitute 7 for x and 38 for y. 38 = 38 (7, 38) is a solution. 2-1 Ordered Pairs 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 ? Substitute 9 for x and 17 for y. 17 = 48 (9, 17) is not a solution. 2-1 Ordered Pairs 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 1+3 4 (1, 4) 2 2+3 5 (2, 5) 3 3+3 6 (3, 6) 4 4+3 7 (4, 7) Helpful Hint A table of solutions can be set up vertically or horizontally. 2-1 Ordered Pairs 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 1 2 3 6m – 5 6(1) – 5 6(2) – 5 6(3) – 5 n 1 7 13 (m, n) (1, 1) (2, 7) (3, 13) 2-1 Ordered Pairs 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 1+6 7 (1, 7) 2 2+6 8 (2, 8) 3 3+6 9 (3, 9) 4 4+6 10 (4, 10) 2-1 Ordered Pairs 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 1 2 3 4 8m – 2 8(1) – 2 8(2) – 2 8(3) – 2 8(4) – 2 n 6 14 22 30 (m, n) (1, 6) (2, 14) (3, 22) (4, 30) 2-1 Ordered Pairs 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) The wholesale cost of the sweater before tax is $48. Multiply. p = 57.6 The $48 wholesale sweater will cost the customer $57.60, so (48, 57.60) is a solution of the equation. 2-1 Ordered Pairs 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) The wholesale cost of the jacket before tax is $85. Multiply. p = 102 The $85.00 wholesale jacket will cost the customer $102, so (85, 102) is a solution of the equation. 2-1 Ordered Pairs 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) The price of the item before tax is $22. Multiply. c = 23.65 After sales tax, the $22 item will cost $23.65, so (22, 23.65) is a solution to the equation. 2-1 Ordered Pairs 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) The price of the item before tax is $10. Multiply. c = 10.75 After sales tax, the $10 item will cost $10.75, so (10, 10.75) is a solution to the equation. 2-1 Ordered Pairs Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 2-1 Ordered Pairs Lesson Quiz: Part I Determine whether each ordered pair is a solution of y = 4x – 7. 1. (2, 15) no 2. (4, 9) yes 3. Use the given values to make a table of solutions. y = 4x 6 for x = 2, 4, 6, 8, and 10 x 4x – 6 y (x, y) 2 4(2) – 6 2 (2, 2) 4 4(4) – 6 10 (4, 10) 6 4(6) – 6 18 (6, 18) 8 4(8) – 6 26 (8, 26) 10 4(10) – 6 34 (10, 34) 2-1 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 2-1 Ordered Pairs Lesson Quiz for Student Response Systems 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) 2-1 Ordered Pairs Lesson Quiz for Student Response Systems 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) 2-1 Ordered Pairs Lesson Quiz for Student Response Systems 3. Use the given values to identify the table of solutions. y = 6x – 4 for x = 1, 3, 5, 7, and 9 A. B. 2-1 Ordered Pairs Lesson Quiz for Student Response Systems 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