Pg. 30 #19-45 ANSWERS

Pre-Algebra 1-7 Ordered Pairs Pre-Algebra 1-7 Ordered Pairs Pre-Algebra: 1-7 HW Page 36 #17-31 all

Pre-Algebra 1-7 Ordered Pairs 1-7 Ordered Pairs Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Pre-Algebra 1-7 Ordered Pairs Warm Up Solve. x = 27 a = 7 n = 17 c = 13 y = 3 Pre-Algebra 1-7 Ordered Pairs 5. 17y + 7 = c  7 = n = = a  2 1. x  8 = 19

Pre-Algebra 1-7 Ordered Pairs Problem of the Day A moving van travels 50 miles per hour. Use the equation y = 50x. How far will the van travel in 4.5 hours? 225 miles

Pre-Algebra 1-7 Ordered Pairs Today’s Learning Goal Learn to write solutions of equations in two variables as ordered pairs.

Pre-Algebra 1-7 Ordered Pairs Vocabulary ordered pair

Pre-Algebra 1-7 Ordered Pairs A sign at the store reads “Birthday Banners $8. Personalize for $1 per letter.” Cecilia has 7 letters in her name, and Dowen has 5 letters in his. Figure out how much it will cost to get a personalized birthday banner for each of them.

Pre-Algebra 1-7 Ordered Pairs Let y be the price of the banner and x be the number of letters in the name; the equation for the price of a banner is y = 8 + x. For Cecelia’s banner: Price of banner = $8 + $1 Number of letters in name For Dowen’s banner: x = 7, y = or y = 15 x = 5, y = or y = 13

Pre-Algebra 1-7 Ordered Pairs A solution of a two-variable equation is written as an ordered pair. When the numbers in the ordered pair are substituted in the equation, the equation is true. (7, 15) is a solution  15 = (5, 13) is a solution  13 = (x, y)  Ordered pair

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair is a solution of y = 4x – 1. Additional Example 1A: Determining If an Ordered Pair Is a Solution of an Equation A. (3, 11) y = 4x – 1 11 = 4(3) – 1 ? Substitute 3 for x and 11 for y. 11= 11 ?  (3, 11) is a solution. A solution since 11=11.

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair is a solution of y = 4x – 1. Additional Example 1B: Determining If an Ordered Pair Is a Solution of an Equation B. (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.

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair is a solution of y = 4x – 1. Additional Example 1C: Determining If an Ordered Pair Is a Solution of an Equation C. (11, 43) y = 4x – 1 43 = 4(11) – 1 ? Substitute 11 for x and 43 for y. 43 = 43 ?  (11, 43) is a solution. A solution since 43 = 43.

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair is a solution of y = 5x + 3. Try This: Example 1A A. (7, 38) y = 5x = 5(7) + 3 ? Substitute 7 for x and 38 for y. 38 = 38 ?  (7, 38) is a solution.

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair is a solution of y = 5x + 3. Try This: Example 1B B. (9, 17) y = 5x = 5(9) + 3 ? Substitute 9 for x and 17 for y. 17 = 48 ?  (9, 17) is not a solution.

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair is a solution of y = 5x + 3. Try This: Example 1C C. (10, 53) y = 5x = 5(10) + 3 ? Substitute 10 for x and 53 for y. 53 = 53 ?  (10, 53) is a solution.

Pre-Algebra 1-7 Ordered Pairs Use the given values to make a table of solutions. Additional Example 2A: Creating a Table of Ordered Pair Solutions A. y = 7x for x = 1, 2, 3, 4 x7x7xy(x, y) (1)7(1, 7) 7(2)14(2, 14) 7(3)21(3, 21) 7(4)28(4, 28)

Pre-Algebra 1-7 Ordered Pairs Use the given values to make a table of solutions. Additional Example 2B: Creating a Table of Ordered Pair Solutions B. n = 6m – 5 for m = 1, 2, 3, (1) – 56(2) – 56(3) – (1, 1) (2, 7) (3, 13) (4, 19) 6(4) – 5 m123 6m – 5 n (m, n) 4

Pre-Algebra 1-7 Ordered Pairs Use the given values to make a table of solutions. A. y = 6x for x = 1, 2, 3, 4 x6x6xy(x, y) (1)6(1, 6) 6(2)12(2, 12) 6(3)18(3, 18) 6(4)24(4, 24) Try This: Example 2A

Pre-Algebra 1-7 Ordered Pairs Use the given values to make a table of solutions. B. n = 8m – 2 for m = 1, 2, 3, (1) – 28(2) – 28(3) – (1, 6) (2, 14) (3, 22) (4, 30) 8(4) – 2 m123 8m – 2 n (m, n) 4 Try This: Example 2B

Pre-Algebra 1-7 Ordered Pairs A salesman wants to make a 20% profit on everything he sells. The equation for the sales price p is p = 1.2w, where w is wholesale cost. Additional Example 3: Retail Application A. What will be the sales price of a sweater with a wholesale cost of $48? p = 1.2(48) p = 57.6 The sweater is $48, and after tax it will cost $57.60, so (48, 57.60) is a solution of the equation. The price of the sweater before tax is $48.

Pre-Algebra 1-7 Ordered Pairs A salesman wants to make a 20% profit on everything he sells. The equation for the sales price p is p = 1.2w, where w is wholesale cost. Additional Example 3 Continued B. What will be the sales price of a jacket with a wholesale cost of $85? p = 1.2(85) p = 102 The jacket is $85.00, and after tax it will cost $102, so (85, 102) is a solution of the equation. The price of the jacket before tax is $85.

Pre-Algebra 1-7 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 percent, the equation for total cost is c = 1.075p, where p is the price before tax. Try This: Example 3A A. How much will a $22 item cost after sales tax? c = 1.075(22) c = 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.

Pre-Algebra 1-7 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 percent, the equation for total cost is c = 1.075p, where p is the price before tax. Try This: Example 3B B. How much will a $10 item cost after sales tax? c = 1.075(10) c = 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.

Pre-Algebra 1-7 Ordered Pairs Lesson Quiz Determine whether each ordered pair is a solution for y = 4x  (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 x4x – 6y(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)