Line of Best Fit Notes Answer Key

Main Ideas/Questions Notes/Examples Line of Best Fit Date: Class: A line drawn on a scatterplot that is close to most of the data points. Can be used to estimate data Example: The graph below shows the relationship between minutes spent studying and the test scores for a math class. Which line best represents the data? Graph each line to justify your answer. 100 90 80 188 Test Score 20 DAAB A Line A: y = 2/3 * x + 50 Line B: y = 3/2 * x + 50 Line C: Line D: y = 3/2 * x + 55 Finding the Line of Best Fit Examples 2 10 20 30 40 50 60 Study Time (minutes) Draw a line that is close to most data points. It should "split" the data. Find the slope between any two points on the line. (Use the slope formula!) 3 Identify the y-Intercept, the point where the line intersects the y-axis. 4 Write the equation in slope-intercept form \{y = mux + b\} where m is the is the slope and b is the y-intercept. 1. The graph below shows the ages and weights of twelve babies. Weight (pounds) 28 22 16 10 a) Write an equation for the line of best fit. (0,7) and (7.18) *Answers may vary 2 4 6 8 10 12 Age (months) b) Estimate the weight of a baby that is 12 months old. (x = 12) y = 11/7 * (12) + 7 \approx 26lb 2. Beth started a new bank account. The graph below shows the monthly balance of the account in its first year. Account Balance ($) 700 600 500 400 300 2 4 6 8 10 12 Months 3. A 10-inch tall candle is lit. The graph below shows its height after each hour. 10 8 a) Write an equation for the line of best fit. (0,350) and (7,470) y = 120/7 * x + 350 *Answers may vary b) Estimate the balance of the account after two years. (x = 24) y = 120/7 * (24) + 350 ~$161.43 a) Write an equation for the line of best fit. (0,10) and (3,9) b = 10 m = (9 - i * 0)/(3 + 0) = (- i)/3 Height of Candle 4 2 2 4 6 8 10 12 Hours 4. The table to the left shows Nick's weight each week into his diet. Make a scatter plot of this data. y = - 1/3 * x + 10 *Answers may vary b) Estimate the height of the candle after 15 hours. (x = 15) y = - 1/3 * (15) + 10 = boxed 5in a) Write an equation for the line of best fit. (3,233) and (7,225) M = (225 - 233)/(7 - 3) = - 8/4 = - 2 b = 240 Time (weeks) Weight (lbs) 1 238 2 235 Z 3 233 4 231 5 228 6 227 Weight (lbs.) 240 230 7 225 220 8 222 9 220 2p 10 217 209 2 4 6 8 10 Time (weeks) 12 y = - 2x + 240 b) Estimate Nick's weight after 24 weeks. (x = 24) Y = - 2(24) + 240 = boxed 192 1b