274 Chapter 3 Graphing Linear Equations in Two Variables 11. Veterinarians keep records of the weights of animals that are brought in for examination. Grindel, the cat, weighed 42 oz when she was 70 days old. She weighed 46 oz when she was 84 days old. Her sister, Frisco, weighed 40 oz when she was 70 days old and 48 oz at 84 days old. 50 Weight vs. Age (70, 42) (84, 48) (84, 46) (70, 40) 40 30 20 10 y 0 65 70 75 80 85 Weight (oz) Age (days) x Grindel Frisco a. Compute the slope of the line representing Grindel’s weight. b. Compute the slope of the line representing Frisco’s weight. c. Interpret the meaning of each slope in the context of this problem. at a rate of 2 oz in 7 days. m 47 means that Frisco’s weight increased at a rate of 4 oz in 7 days. d. Which cat gained weight more rapidly during this time period? Frisco gained weight more rapidly. 12. The graph depicts the rise in the number of jail inmates in the United States since 2000. Two linear equations are given: one to describe the number of female inmates and one to describe the number of male inmates by year. Let y represent the number of inmates (in thousands). m 27 m 47 m means that Grindel’s weight increased 27 800 Number of Inmates (in thousands) Number of Jail Inmates by Year y 5 19.2x 1 544 700 600 500 400 300 200 100 y Let x represent the number of years since 2000. a. What is the slope of the line representing the number of female inmates? Interpret the meaning of the slope in the context of this problem. m 4. inmates has increased by 4 thousand per year since 2000. b. What is the slope of the line representing the number of male inmates? Interpret the meaning of the slope in the context of this problem. c. Which group, males or females, has the larger slope? What does this imply about the rise in the number of male and female prisoners? Males. The number of male inmates is increasing at a faster rate than the number of female inmates. d. Assuming this trend continues, use the equation to predict the number of female inmates in 2015. 131 thousand or 131,000 y 5 4.0x 1 71 0 0 2 4 6 8 10 12 Year (x 5 0 corresponds to 2000) Male Inmates Female Inmates (Source: U.S. Bureau of Justice Statistics) m 19.2. The number of female 13. The electric bill charge for a certain utility company is $0.095 per kilowatt-hour plus a fixed monthly tax of $11.95. The total cost, y, depends on the number of kilowatt-hours, x, according to the equation y 0.095x 11.95, x 0 . a. Determine the cost of using 1000 kilowatt-hours. $106.95 b. Determine the cost of using 2000 kilowatt-hours. $201.95 c. Determine the y-intercept. Interpret the meaning of the y-intercept in the context of this problem. d. Determine the slope. Interpret the meaning of the slope in the context of this problem. x The number of male inmates has increased by 19.2 thousand per year since 2000. (0, 11.95). For 0 kilowatt-hours used, the cost consists of only the fixed monthly tax of $11.95. m 0.095. The cost increases at a rate of $0.095 for each kilowatt-hour used. Writing Translating Expression Geometry Scientific Calculator Video
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