Name Class Date Practice 14-5 Linear Models Fitting a Straight Line 14-5 Linear Models Fitting a Straight Line 1. Which of the lines shown is a reasonable trend line for the scatter plot? 2. Which of the lines shown is a reasonable trend line for the scatter plot? g f p x z s 3. The scatter plot suggests a linear association among the data. Two points that lie on the trend line drawn for the data are (2,18) and (4,24). Find the equation for the trend line. 4. The scatter plot suggests a linear association among the data. Two points that lie on the trend line drawn for the data are (3,34) and (5,26). Find the equation for the trend line. A. y = 4x + 13 B. y = 3x + 13 C. y = 3x + 12 D. y = 4x + 11 A. y 5x + 46 B. y 4x + 46 C. y 4x + 47 D. y 5x + 45 Practice 14-5 1 Homework G
5. The scatter plot suggests a linear association among the data. Find an approximate equation for the trend line drawn for the data. 6. The scatter plot suggests a linear association among the data. Find an approximate equation for the trend line drawn for the data. A. y = 5x + 21 B. y = 6x + 18 C. y = 6x + 21 D. y = 5x + 18 A. y 3x + 40 B. y 2x + 40 C. y 2x + 37 D. y 3x + 37 7. Writing The scatter plot shows Maria s distance from her house during the first hour of her drive home from the beach. The plot suggests a linear association among the data. a) Find an approximate equation for the trend line drawn. A. y 1.07x + 96.6 B. y 0.8x + 96.6 C. y 1.07x + 94 D. y 0.8x + 94 b) Does this plot suggest a positive or negative association? How can you tell? Describe three other associations of this type that might occur in the real world. Practice 14-5 2 Homework G
8. Reasoning The scatter plot shows the average height of people ages 2 12 in a certain country. a) Which of the lines shown is a reasonable trend line for the scatter plot? A. line f f s m z B. line m C. line z D. line s b) How can a scatter plot have more than one linear model? How do you decide which model to use? Explain your reasoning. 9. Error Analysis The scatter plot shows the balance of Anthony s bank account during the past 60 days. The plot suggests a linear association among the data. Two points that lie on the trend line drawn are (10,264) and (50,160). Anthony incorrectly claims that y 5 x + 290 is an approximate equation for 13 the trend line. a) Find an approximate equation for the trend line drawn. A. y 13 5 x + 290 C. y 13 5 x + 276 B. y 9 x + 273 4 D. y 9 x + 287 4 b) What error might Anthony have made? A. He swapped the numerator and the denominator for the slope. B. He used the incorrect sign for the slope. C. He used the incorrect sign for the y-intercept. D. He swapped the x- and y-coordinates while finding the y-intercept. 10. Theme Parks The scatter plots suggest a linear trend in the attendance at theme parks in a certain country over time since 1988. Find an approximate equation for the trend line drawn for the data. A. y = 5.92x + 238.16 B. y = 5.92x + 233.16 C. y = 4.21x + 270.48 D. y = 4.21x + 244.06 Practice 14-5 3 Homework G
11. Mental Math The scatter plot shows Leanna s elevation above sea level during her hike from the base to the top of a mountain. The plot suggests a linear association among the data. Two points that lie on the trend line drawn are (30,1070) and (75,1680). a) Find an approximate equation for the trend line drawn. A. y = 15.25x + 613 B. y = 13.56x + 625 C. y = 13.56x + 663 D. y = 15.25x + 536 b) Use mental math to find a similar equation if the base was 100 ft higher above sea level. A. y = 13.56x + 763 B. y = 113.56x + 513 12. Estimation The scatter plot shows the daily high temperatures in a city over the past 180 days. The plot suggests a linear association among the data. Two points that lie on the trend line drawn for the data are (49,71) and (163,29). Estimate an equation for the trend line drawn by first rounding each of the coordinates to the nearest 10. A. y 0.36x + 86.9 B. y 0.33x + 86.5 C. y 0.36x + 88.0 D. y 0.33x + 82.8 13. The scatter plot suggests a linear trend in the number of houses on a certain street since the street was built in 2003. Find an approximate equation for the trend line. A. y = 7.17x + 5.1 B. y = 5.07x + 5.1 C. y = 5.07x + 8.8 D. y = 7.17x + 8.8 C. y = 113.56x + 636 D. y = 13.56x + 525 Practice 14-5 4 Homework G
14. Challenge The scatter plot shows the elevation of an airplane as it starts to descend toward the ground. The plot suggests a linear association among the data. Two points that lie on the trend line drawn are (30,17774) and (60,2792). a) Find an approximate equation for the trend line. A. y 483.29x + 32,273 B. y 499.40x + 33,286 C. y 499.40x + 32,756 D. y 483.29x + 31,789 b) Find a similar equation if the plane descended at a rate 1.3 times as fast from an elevation 3,000 ft lower. A. y 499.40x + 35,756 B. y 649.22x + 29,756 C. y 499.40x + 29,756 D. y 649.22x + 35,756 15. Challenge The scatter plot shows the rate at which snow fell during each hour in the final six hours of a 12-hour snow storm. The plot suggests a linear association among the data. a) Find an approximate equation for the trend line drawn. A. y 0.167x + 2.03 B. y 0.235x + 2.12 C. y 0.235x + 2.38 D. y 0.167x + 2.38 b) Describe a method to estimate the total amount of snow that fell during the final six hours. Then use your method to estimate the total amount. Practice 14-5 5 Homework G
ANSWER KEY Practice 14-5: Linear Models Fitting a Straight Line 1. line f 2. line p 3. C 4. B 5. D 6. D 7. a) D b) Answers will vary 8. a) B b) Answers will vary 9. a) A b) A 10. A 11. a) C b) A 12. C 13. D 14. a) C b) B 15. a) A b) Answers will vary Practice 14-5 6 Answer Key G