154 CHAPTER 3 Linear and Quadratic Functions 8. 5 20 55 35 9. 0 0 25 10 10. 0 0 35 45 In Problems 11–16: (a) Draw a scatter plot. (b) Select two points from the scatter plot, and find an equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter plot. (d) Use a graphing utility to find the line of best fit. (e) What is the correlation coefficient r? (f) Use a graphing utility to draw the scatter plot and graph the line of best fit on it. 11. x 345 6789 y 4 6 7 10121416 12. x 3 5 7 9 11 13 y 0236 911 13. x −2 −1 0 1 2 y −4 01 4 5 14. x −2 −1 0 1 2 y 7 6 3 2 0 15. x −20 −17 −15 −14 −10 y 100 120 118 130 140 16. x −30 −27 −25 −20 −14 y 10 12 13 13 18 17. Candy The following data represent the weight (in grams) of various candy bars and the corresponding number of calories. Hershey’s Milk Chocolate® Nestle’s Crunch® Butterfinger® Baby Ruth® Almond Joy® Twix® (with caramel) Snickers® Heath® 44.28 44.84 61.30 66.45 47.33 58.00 61.12 39.52 230 230 270 280 220 280 280 210 Source: Megan Pocius, student at Joliet Junior College. Calories, y Weight, x Candy Bar (a) Draw a scatter plot of the data, treating weight as the independent variable. (b) What type of relation appears to exist between the weight of a candy bar and the number of calories? (c) Select two points and find a linear model that contains the points. (d) Graph the line on the scatter plot drawn in part (a). (e) Use the linear model to predict the number of calories in a candy bar that weighs 62.3 grams. (f) Interpret the slope of the line found in part (c). 18. Tornadoes The following data represent the width (in yards) and length (in miles) of various tornadoes. Width (yards), w Length (miles), L 200 2.5 350 4.8 180 2.0 300 2.5 500 5.8 400 4.5 500 8.0 800 8.0 100 3.4 50 0.5 700 9.0 600 5.7 Source: NOAA. (a) Draw a scatter plot of the data, treating width as the independent variable. (b) What type of relation appears to exist between the width and the length of tornadoes? (c) Select two points and find a linear model that contains the points. (d) Graph the line on the scatter plot drawn in part (a). (e) Use the linear model to predict the length of a tornado that has a width of 450 yards. (f) Interpret the slope of the line found in part (c). Applications and Extensions
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