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Name ________________________________________ Date __________________ Class__________________ LESSON 5-1 Reading Strategy Compare and Contrast Variations can be direct variations or inverse variations. In direct variation, y varies directly as x: y kx The graph of direct variation is a straight line. In inverse variation, y varies inversely as x: k y x The graph of inverse variation is undefined when x 0. Determine whether each represents direct or inverse variation. 1. The number of pancakes made and the amount of pancake mix used ______________ 2. The price of milk and the number of gallons you can buy for $20.00 ______________ 3. The outside temperature in the winter and the amount of fuel required to heat a house ______________ 4. A child’s age and his height ______________ 5. The number of apples purchased and the total cost ______________ Answer each question. 6. a. Kelly runs for exercise. Explain how the distance she runs varies as her running speed. _____________________________________________________________________________________ b. Write an equation showing the relationship between the distance she runs, d, and her running speed, s. 7. _______________________ a. Cal made some pizzas for his party. Explain how the number of slices per person varies as the number of people at the party. _____________________________________________________________________________________ b. Write an equation showing the relationship between the number of slices per person, p, and the number of people at the party, n. _______________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 5-10 Holt McDougal Algebra 2 3. $3.00 Problem Solving 4. 15 h 5. 8 bushels 1. a. t = 6. 234 trillionths of a cm b. k = 975 Reteach c. It is the total number of student hours that it takes to build a 7-foot sailboat. 1. a. k = 1.5 b. y = 1.5x d. 81.25 h c. y = 1.5x; y = 1.5 ⋅ 50; y = 75 2. 13 students 2. a. y = kxz; 150 = k ⋅ 2.5 ⋅ 12; 150 = 30k, k=5 b. y = 5xz b. y = 3. C 4. B 5. D 6. B Reading Strategies c. y = 5xz; y = 5 ⋅ 4 ⋅ 6.5; y = 130 3. a. y = k s k k ; 2 = ; k = 18 x 9 1. Direct 2. Inverse 3. Inverse 4. Direct 18 x 5. Direct 6. a. As her speed increases, the number of miles she runs increases, so it is direct variation. 18 18 ;y = ;y =3 c. y = x 6 b. d = ks 7. a. As the number of people at the party increases, the number of slices per person decreases, so it is inverse variation. b. p = k n 5-2 MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Practice A Challenge 1. F = 1. Possible answer: If the denominator is 0, then the expression is undefined because division by 0 is impossible. Gm1m2 r2 2. About 6.67 × 10−11Nm2per kg2 2. x = 3 kv 2 3. About 4.43 × 10 N 4. H = r −7 1 5. Reduce the resistance by a factor of . 3 6. Double the voltage. k T 7. F = L 8. It would increase by a factor of 2. 9. The length could be doubled or the tension cut by a factor of 4. 3. 5 ;x≠0 x2 4. x+3 ;x≠0 x2 5. 2 ; x ≠ −3 3 6. 2x + 7 ; x ≠ −3 x+3 7. 3x y2 8. 2x 4 3y 2 9. 4 x−2 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A55 Holt McDougal Algebra 2