Core Focus on Linear Equations Lesson 5.5 Core Focus on Linear Equations Predicting with Best Fit Equations

Warm-Up y = −3x + 36 x: 1 ~ 3 ~ 8 ~ 11 ~ 14 y: 9 ~ 11 ~ 19 ~ 23 ~ 28 1. Find the equation for the line through Q-points (4, 24) and (10, 6). 2. Use the following table to answer the questions below. a) Make a scatter plot of the data. b) Find the five-number summary for the x-values and the y-values. c) Draw in horizontal and vertical lines based on the quartiles. d) What are the ordered pairs for the two Q-points that best follow the data? y = −3x + 36 x 1 3 8 10 11 14 y 9 15 19 23 22 28 x: 1 ~ 3 ~ 8 ~ 11 ~ 14 y: 9 ~ 11 ~ 19 ~ 23 ~ 28 (3, 11) and (11, 23)

Predicting With Best Fit Equations Lesson 5.5 Predicting With Best Fit Equations Use equations based on data to make predictions and judge the reasonableness of predictions.

Example 1 Use the equation and given value to solve for the value of the missing variable. a. y = 2x – 8 x = 11, y =_____ Write the original equation. y = 2x – 8 Substitute 11 for x in the equation. y = 2(11) – 8 Simplify. y = 22 – 8 y = 14

Example 1 Use the equation and given value to solve for the value of the missing variable. b. T = 40 + 1.6d T = 65, d = _____ Write the original equation. Substitute 65 for T in the equation. Subtract 40 from both sides of the equation. Divide both sides by 1.6. T = 40 + 1.6d 65 = 40 + 1.6d –40 –40 a 25 = 1.6d a 1.6 1.6 a 15.625 = d a

Example 2 A grocery store manager tracked the cost of a gallon of milk for the last several months of 2011. The line of best fit models the price, P, based on the number of months (m) since December 2011: P = 3.60 + 0.04m. a. What value of m would represent January 2013? January 2013 is a full year (12 months) plus a month after December 2011, so m = 13. b. Use the equation P = 3.60 + 0.04m to predict the price of a gallon of milk at this store in January 2013. January 2013 means m = 13. Substitute 13 into the equation for m. P = 3.60 + 0.04(13) P = 3.60 + 0.52 Evaluate the equation. P = $4.12 A gallon of milk will cost $4.12 in January 2013.

Example 2 A grocery store manager tracked the cost of a gallon of milk for the last several months of 2011. The line of best fit models the price, P, based on the number of months (m) since December 2011: P = 3.60 + 0.04m. c. How many months after December 2011 will a gallon of milk first cost more than $5.00 at this store? The price of milk is $5.00. Substitute 5.00 for P and solve for m. Subtract 3.60 from both sides. Divide both sides by 0.04. After 35 months, milk will cost $5.00 at this grocery store. P = 3.60 + 0.04m 5.00 = 3.60 + 0.04m –3.60 –3.60 a 1.40 = 0.04m a 0.04 0.04 a 35 = m a

Example 3 Cybil works in the maternity section of the hospital as a nurse. She determined that a baby’s weight in pounds (P) can be modeled by P = 7.2 + 0.6w, where w is the baby’s age in weeks. Does this model seem reasonable for a one-year old baby? A one-year old baby is 52 weeks old. P = 7.2 + 0.6w Evaluate the equation for w = 52. P = 7.2 + 0.6(52) P = 7.2 + 31.2 P = 38.4 pounds A weight of 38.4 pounds is far too heavy for a 1-year old baby. This model may only be reasonable for the first few months after a baby’s birth.

Communication Prompt Describe how an equation for a line of best fit can be used to make predictions. Is it more reliable to use an equation for a line of best fit or to extend a line of best fit as you learned in Lesson 5.2? Explain.

Exit Problems Use the equation and given value to solve for the value of the missing variable. 1. y = 1.2x + 18 y = 45.6, x = ___ 2. V = 25 + 3.5x x = 15, V = ___ Rachel has found that the time it takes for her to make her favorite dessert decreases the more times she makes it. The time it takes in minutes (M) can be modeled by: M = 72 – 0.75n, where n is the number of times that Rachel has made the dessert. a. How long will it take Rachel to make her dessert the fifth time? b. After how many times will Rachel be able to make her dessert in 63 minutes? c. How long will it take Rachel to make her dessert the 40th time? Do you think this is reasonable? 23 77.5 68.25 minutes 12 times 42 minutes. This may or may not be reasonable, depending on baking time.