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DO NOT EDIT--Changes must be made through "File info" CorrectionKey=B DO NOT EDIT--Changes must be made through "File info" CorrectionKey=B EXAMPLE 2 Tim is paid $8 more than the number of bags of peanuts he sells at the baseball stadium. The table shows the relationship between the money Tim earns and the number of bags of peanuts Tim sells. Identify the independent and dependent variables, and write an equation that represents the relationship. Bags of peanuts, x 0 1 2 Money earned, y 8 9 10 11 7. Use the data in the table to write an equation to express y in terms of x. Then graph the equation. (Lessons 12.3, 12.4) 1. y (-1, 4) 4 3. (-1, 4) (-3, -1) O 2 5 6 7 2 O x 1 2 3 4 5 205 + 2d Suntracker: 195 + 2.5d; after 22 days: Suntracker: h = 195 + 2.5(22) = 250; Sunny Yellow: h = 205 + 2(22) = 249. Suntracker is taller. 8 2. Vernon practiced soccer 5_43 hours this week. He practiced 4_13 hours on weekdays and the rest over the weekend. 6 4 a. Write an equation that represents the situation. Define your variable. Let w = the number of hours Vernon practiced soccer over the 2 2 4 6 Time (h) 4. What is the independent variable? 5. What is the dependent variable? 8 weekend; 4_13 + w = 5_34 10 b. What is the least common multiple of the denominators of 5_34 and 4_13 ? Show your work. time Using prime factorization: 4 = 2 × 2; 3 = 3; LCM = (2)(2)(3) = 12 distance © Houghton Mifflin Harcourt Publishing Company Distance (km) 4 c. The Suntracker grows at a rate of 2.5 centimeters per day after the first 60 days. If this sunflower is 195 centimeters tall when it is 60 days old, write an expression to represent Suntracker’s height after d days. Which sunflower will be taller after 22 days, or when it is 82 days old? Explain how you found your answer. 10 © Houghton Mifflin Harcourt Publishing Company 4 y 15 days; 235 = 205 + 2d; 30 = 2d; 15 = d ̵2 Use the graph to answer the questions. (Lesson 12.2) c. Solve the equation and interpret the solution. Show your work. 5 9 9 4 4 4_13 + w = 5_34; 4__ + w = 5__ ; w = 5__ - 4__ = 1__ 12 12 12 12 12 6. Describe the relationship between the independent variable and the dependent variable. 5 hours over the weekend. Vernon practiced 1__ 12 The dependent variable is 3 times the independent variable. Unit 5 6A_MFLESE200906_U5SG.indd 361 3 CAREERS IN MATH Botanist Dr. Adama is a botanist. She measures the daily height of a particular variety of sunflower, Sunny Yellow, beginning when the sunflower is 60 days old. At 60 days, the height of the sunflower is 205 centimeters. Dr. Adama finds that the growth rate of this sunflower is 2 centimeters per day after the first 60 days. 4 ̵4 O 2 b. How many days does it take for the sunflower to reach 235 centimeters? Show your work. x ̵2 ̵4 1 a. Write an expression to represent the sunflower’s height after d days. (4, 4) 2 0 Unit 5 Performance Tasks EXERCISES Graph and label each point on the coordinate plane. (Lesson 12.1) 2. (-3, -1) x y= x+4 The equation y = x + 8 expresses the relationship between the number of bags Tim sells and the amount he earns. 1. (4, 4) 8 6 The number of bags is the independent variable, and the money Tim earns is the dependent variable. 3 y 10 361 4/17/14 11:53 PM 362 Unit 5 6A_MFLESE200906_U5SG.indd 362 4/17/14 11:53 PM Equations and Inequalities 362