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Name LESSON Date Class Practice C 2-7 Equations in Two Variables Write an equation in two variables that gives the values in each table, and then find the missing terms. 1. 2. 3. 4. x 3 4 5 6 25 36 y 4 9 x 32 28 y 8 6 5 4 x 1 3 4 5 y 7 12 17 22 8 6 4 2 1.6 0.8 x y 4 24 16 3.2 Write an equation for the relationship. Tell what each variable you use represents. 5. The rate of travel is the quotient of the distance traveled divided by the time spent traveling. 6. A taxi driver charges a flat rate of $3.00 and $0.80 per mile traveled. 7. Tony earns $12 per hour for 40 hours a week. For any hour over 40, he earns time and a half, which is the sum of the regular hourly rate and half that rate. Use your equation to find how much Tony will earn if he works 45 hours next week. 8. Explain why the equation y x 2 can have two possible values of x for every value of y. Copyright © by Holt, Rinehart and Winston. All rights reserved. 59 Holt Mathematics Practice B 2-7 Equations in Two Variables Practice A 2-7 Equations in Two Variables LESSON LESSON Write an equation in two variables that gives the values in each table. Use the equation to find the value of y for the indicated value of x. Write an equation in two variables that gives the values in each table. 1. 2. x 0 1 2 3 y 2 3 4 5 x 1 2 3 4 y 5 10 15 20 yx2 1. y 5x 2. Circle the letter of the equation that correctly describes each relationship. 3. Carol is 4 years younger than her brother, Vishu. Let c Carol’s age and v Vishu’s age. C cv÷4 A cv4 B c 4v D c4v 4. If Vishu is 10 years old, how old is Carol? F 14 years old H 6 years old 5. Tim earns $9 for every hour that he works. Let h the number of hours Tim works and m amount earned. A mh9 C mh÷9 D m9h B m 9h 6. If Tim works 18 hours in one week, how much will he earn in all? F $27 H $2 G $9 J $162 G 40 years old 3. 4. 1 J 22 years old x 1 2 3 4 5 y 7 14 21 28 ♦ x 2 3 4 5 6 y 3 2 1 0 ♦ x 20 16 12 8 4 y 10 8 6 4 ♦ x 7 8 9 10 11 y 11 12 13 14 ♦ y 7x y 35 yx5 y1 yx2 y2 yx4 y 15 Write an equation for the relationship. Tell what each variable you use represents. 5. Amanda is 7 years younger than her cousin. Possible answer: y x 7; y Amanda’s age; x her cousin’s age 6. The population of North Carolina is twice as large as the population of South Carolina. Write an equation for the relationship. Tell what each variable you use represents. Possible answer: n 2s; n population of North Carolina; 7. An extra-large pizza costs $7 more than a personal-size pizza. Write an equation for this relationship. Tell what each variable you use represents. s population of South Carolina 7. An Internet book company charges $7 for each paperback book, plus $2.75 for shipping and handling per order. Possible answer: y 7 x ; y price of extra-large pizza; x price of personal-size pizza Possible answer: y 7x 2.75; y total price of order; 8. On average, Tamara jogs 10 miles per hour. Write an equation to show how far Tamara runs in h hours. Tell what each variable you use represents. x number of books purchased 8. Henry records how many days he rides his bike and how far he rides each week. He rides the same distance each time. He rode 18 miles in 3 days, 24 miles in 4 days, and 42 miles in 7 days. Write an equation in two variables for the relationship. Possible answer: y 10h, y distance run; h hours run m 6d; m miles, and d days 57 Copyright © by Holt, Rinehart and Winston. All rights reserved. Holt Mathematics Practice C 2-7 Equations in Two Variables LESSON In the table below, the x-values are the input and the y-values are the output. Write an equation in two variables that gives the values in each table, and then find the missing terms. 2. 3. 4. Holt Mathematics Review for Mastery 2-7 Equations in Two Variables LESSON 1. 58 Copyright © by Holt, Rinehart and Winston. All rights reserved. x 2 3 4 5 6 y 4 9 16 25 36 x 32 28 24 20 16 y 8 7 6 5 4 x 1 2 3 4 5 y 7 12 17 22 27 x 10 8 6 4 2 y 4 3.2 2.4 1.6 0.8 yx2 x 0 1 2 3 4 5 y 4 5 6 7 8 9 10 ? 6 7 To write an equation in two variables for a table of values, first compare the x- and y-values to find a pattern. Each y-value is 4 more than its corresponding x-value. y x (4) Then use the pattern to write a rule for the table. y 5x 2 yx4 You can use the rule to find a missing value in a table. To find the value of y in table above when x 7, substitute 7 for x in the equation. y 0.4x Write an equation for the relationship. Tell what each variable you use represents. yx4 y74 y 11 So y is 11 when x is 7. Write an equation in two variables that gives the values in each table. Use the equation to find the value of y for the indicated value of x. 5. The rate of travel is the quotient of the distance traveled divided by the time spent traveling. 1. Possible answer: r d t; r rate; d distance; t time 6. A taxi driver charges a flat rate of $3.00 and $0.80 per mile traveled. x 1 2 3 6 2. x 18 17 16 15 14 13 y 3 6 9 12 15 ? y 15 14 13 ? 11 10 4 5 y 3x, y 18 Possible answer: c 3 0.8m; c total charge; m miles y x 3, y 12 You can also write equations for relationships that are described in words. 7. Tony earns $12 per hour for 40 hours a week. For any hour over 40, he earns time and a half, which is the sum of the regular hourly rate and half that rate. Use your equation to find how much Tony will earn if he works 45 hours next week. The length of the pool is 6 times the width of the pool. length of pool w width of pool 6w Possible answer: y 480 18h; y total weekly earnings; h hours worked over 40 hours; $570 Choose variables for the equation. Write an equation. Write an equation for the relationship. Tell what each variable you use represents. 8. Explain why the equation y x 2 can have two possible values of x for every value of y. 3. Todd is 6 inches taller than Scott. 4. Alana is 4 times as old as Tracey. because the positive and negative of a number squared have the same t Todd’s height a Alana’s age value: 4 22; 4 (2)2 s Scott’s height t Tracey’s age ts6 a 4t Copyright © by Holt, Rinehart and Winston. All rights reserved. 59 Copyright © by Holt, Rinehart and Winston. Holt Mathematics Copyright © by Holt, Rinehart and Winston. All rights reserved. 97 60 Holt Mathematics Holt Mathematics