Section 3.6 Applications of Linear Equations and Modeling 275 14. For a recent year, children’s admission to the Minnesota State Fair was $8. Ride tickets were $0.75 each. The equation y 0.75x 8 represented the cost, y, in dollars to be admitted to the fair and to purchase x ride tickets. a. Determine the slope of the line represented by y 0.75x 8. Interpret the meaning of the slope in the context of this problem. m 0.75; The slope means that the cost increases at a rate of 75¢ per ride. (0, 8); The cost was $8 if 0 rides were purchased. b. Determine the y-intercept. Interpret its meaning in the context of this problem. c. Use the equation to determine how much money a child needed for admission and to ride 10 rides. $15.50 Concept 2: Writing a Linear Model Using Observed Data Points 15. Meteorologists often measure the intensity of a tropical storm or hurricane by the maximum sustained wind speed and the minimum pressure. The relationship between these two quantities is approximately linear. Hurricane Katrina had a maximum sustained wind speed of 150 knots and a minimum pressure of 902 mb (millibars). Hurricane Ophelia had maximum sustained winds of 75 knots and a pressure of 976 mb. (See Example 2.) a. Find the slope of the line between these two points. Round to one decimal place. m 1.0 1000 800 600 b. Using the slope found in part (a) and the point (75, 976), find a linear model that represents the minimum pressure of a hurricane, y, versus its maximum sustained wind speed, x. y x 1051 c. Hurricane Dennis had a maximum wind speed of 130 knots. Using the equation you found in part (b), predict the minimum pressure. The minimum pressure was approximately 921 mb. 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. m 3.5. 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. m 21.5 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. y 21.5x 57 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. 272 trillion Btu 1200 Pressure vs. Wind Speed 0 20 40 60 80 100 120 140 160 Pressure (mb) Wind Speed (knots) 400 200 0 y x (150, 902) (75, 976) The slope means that the consumption of wind energy in the United States increased by 21.5 trillion Btu per year. y 90 Height Versus Arm Length 80 0 3 6 9 12 15 18 21 24 Height (inches) Arm Length (inches) 70 60 50 40 30 20 10 0 −10 x (24, 82.25) (17, 57.75) y 3.5x 1.75 73.5 in. or 6 ft 11 2 in. For each additional inch in length of a person’s arm, the person’s height increases by 3.5 in. y x 210 180 150 120 90 Wind Energy Consumption United States, 2000 to 2005 60 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) Writing Translating Expression Geometry Scientific Calculator Video
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