Average Salary for a Public High School Principal 85,000 82,000 79,000 76,000 73,000 70,000 67,000 64,000 61,000 58,000 (5, 66,596) 55,000 (0, 55,722) (11, 83,367) (10, 79,839) (8, 74,380) (9, 76,768) 0 1 2 3 4 5 6 7 8 9 10 11 Year Average salary (in dollars) a) Write a linear equation to model this data. Use the data points for 1990 and 2001. (Round the slope to the nearest whole number.) b) Explain the meaning of the slope in the context of the problem. c) Use the equation to estimate the average salary in 1993. d) If the trend continues, fi nd the average salary in 2005. 109) The chart shows the number of hybrid vehicles registered in the United States from 2000 to 2003. (American Demographics, Sept 2004, Vol 26, Issue 7) Number registered Hybrid Vehicles Registered in the United States 45,000 40,000 35,000 30,000 25,000 20,000 15,000 10,000 5,000 6,479 43,435 34,521 19,033 2000 2001 2002 2003 Year a) Write a linear equation to model this data. Use the data points for 2000 and 2003. Let x represent the number of years after 2000, and let y represent the number of hybrid vehicles registered in the United States. (Round the slope to the tenths place.) b) Explain the meaning of the slope in the context of the problem. c) Use the equation to determine the number of vehicles registered in 2002. How does it compare to the actual number on the chart? d) If the current trend continues, approximately how many hybrid vehicles will be registered in 2010? c) According to the equation, how many people lived in Maine in 1998? in 2002? d) If the current trend continues, in what year would the population be 1,431,900? 106) Since 1997, the population of North Dakota has been decreasing by about 3290 people per year. The population was about 650,000 in 1997. (Statistical Abstract of the United States) a) Write a linear equation to model this data. Let x represent the number of years after 1997, and let y represent the population of North Dakota. b) Explain the meaning of the slope in the context of the problem. c) According to the equation, how many people lived in North Dakota in 1999? in 2002? d) If the current trend holds, in what year would the population be 600,650? 107) The graph here shows the number of farms (in thousands) with milk cows between 1997 and 2002. x represents the number of years after 1997 so that x 0 represents 1997, x 1 represents 1998, and so on. Let y represent the number of farms (in thousands) with milk cows. (USDA, National Agricultural Statistics Service) Number of Farms With Milk Cows (0, 124) (1, 117) (2, 111) (3, 105) 1 2 3 4 Year (4, 98) 5 126 122 118 114 110 106 102 98 94 90 y 0 0 Number of farms (in thousands) (5, 92) x a) Write a linear equation to model this data. Use the data points for 1997 and 2002. b) Explain the meaning of the slope in the context of the problem. c) If the current trend continues, fi nd the number of farms with milk cows in 2004. 108) The graph here shows the average salary for a public school high school principal for several years beginning with 1990. x represents the number of years after 1990 so that x 0 represents 1990, x 1 represents 1991, and so on. Let y represent the average salary of a high school principal. (Statistical Abstract of the United States) www.mhhe.com/messersmith SECTION 4.3 Writing an Equation of a Line 185
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