Section 2.4 Applications of Linear Equations and Modeling 179 Concept 3: Finding a Linear Model from Observed Data Points 15. Windchill is the apparent temperature felt on exposed skin.This is a relationship between air temperature and wind speed. At a fixed air temperature of 5F, windchill temperature is approximately linear for speeds between 10 mph and 110 mph. At 20 mph the windchill is 15F and at 50 mph it is 24F. (See Example 3.) a. Make a graph with wind speed on the x-axis and windchill on the y-axis. Plot the points (20, 15) and (50, 24), and draw the line through the points. Windchill Versus Wind Speed for Fixed Temperature of 5 Fahrenheit 10 20 30 40 50 60 Windchill (°F) Wind Speed (mph) 30 20 10 0 10 20 30 b. Write an equation of the line through the given points. Write the equation in slope-intercept form. c. Use the equation from part (b) to estimate the windchill for a wind speed of 40 mph. d. Use the equation from part (b) to estimate the windchill for a wind speed of 46 mph. e. What is the slope of the line and what does it mean in the context of this problem? 16. During a drought, the average water level in a retention pond decreased linearly with time. 8 7 6 5 4 3 2 0 Water Level Versus Days of Drought (12, 4) a. Let y represent the water level (in feet) and x represent the number of days since the beginning of the drought. Use the ordered pairs given to write a linear equation to estimate the water level based on the number of days since the drought began. b. Use the linear equation to approximate the water level after 15 days. c. Use the linear equation to approximate the water level after 25 days. d. What is the slope of the line and what does it mean in the context of this problem? e. Interpret the meaning of the x-intercept. Do you think that this linear trend will continue indefinitely? Explain your answer. 21 0 5 10 15 20 25 30 Water Level (ft) 1 Number of Days (4, 6) x y
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