258 Chapter 3 Graphing Linear Equations in Two Variables 16. The figure depicts a relationship between a person’s height, y (in inches), and the length of the person’s arm, x (measured in inches from shoulder to wrist). a. Use the points (17, 57.75) and (24, 82.25) to find a linear equation relating height to arm length. b. What is the slope of the line? Interpret the slope in the context of this problem. c. Use the equation from part (a) to estimate the height of a person whose arm length is 21.5 in. 17. Wind energy is one type of renewable energy that does not produce dangerous greenhouse gases as a by-product.The graph shows the consumption of wind energy in the United States for selected years.The variable y represents the amount of wind energy in trillions of Btu, and the variable x represents the number of years since 2000. a. Use the points (0, 57) and (4, 143) to determine the slope of the line. b. Interpret the slope in the context of this problem? c. Use the points (0, 57) and (4, 143) to find a linear equation relating the consumption of wind energy, y, to the number of years, x, since 2000. d. If this linear trend continues beyond the observed data values, use the equation in part (c) to predict the consumption of wind energy in the year 2010. 18. The graph shows the average height for boys based on age. Let x represent a boy’s age, and let y represent his height (in inches). a. Find a linear equation that represents the height of a boy versus his age. b. Use the linear equation found in part (a) to predict the average height of a 5-year-old boy. y 90 Height Versus Arm Length 80 70 60 50 40 30 20 10 0 −10 0 3 6 9 12 15 18 21 24 Height (inches) 210 180 150 120 60 50 40 30 Wind Energy Consumption United States, 2000 to 2005 Concept 3: Writing a Linear Model Given a Fixed Value and a Rate of Change 19. Andrés has a cell phone plan with a local telephone company. His bill is determined each month by a $39.99 flat fee plus $0.20 for each text message sent or received. (See Example 3.) a. Write a linear model to compute the monthly cost, y, of Andrés’ cell phone bill if x text messages are sent or received. b. Use the equation to compute Andrés’ cell phone bill for a month in which he sent or received a total of 40 text messages. Arm Length (inches) 20. Anabel lives in New York and likes to keep in touch with her family in Texas. She uses 10-10-987 to call them. The cost of a long distance call is $0.53 plus $0.06 per minute. a. Write an equation that represents the cost,C, of a long distance call that is x minutes long. b. Use the equation to compute the cost of a long distance phone call that lasted 32 minutes. x (24, 82.25) (17, 57.75) 60 Average Height of Boys Based on Age 0 1 2 3 4 5 6 7 8 9 10 11 12 Height (in.) Age (yr) 20 10 0 y x (8, 51) (2, 36) (Source: National Parenting Council) y x 90 0 0 1 2 3 4 5 6 Energy Use (Trillions of Btu) Year (x 0 corresponds to 2000) 30 (4, 143) (0, 57) (Source: United States Department of Energy)
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