Alg 1 5.4 pg 296

FOCUS ONAPPLICATIONSEXAMPLE 2Approximating a Best-Fitting LineDISCUS EVENTThe discus throw isone of the original Olympicevents. New records for thedistance an athlete canthrow the discus continue tobe set.REALLIFEDISCUS THROWS The winning Olympic discusthrows from 1908 to 1996 are shown in the table.After graphing these data points, draw a line thatcorresponds closely to the data. Write an equationof your line.SOLUTIONLet x represent the years since 1900. Let yrepresent the winning throw. To begin, plot thepoints given by the ordered pairs. Then sketchthe line that appears to best fit the points.Distance (ft)240220200180160140120yWinning Discus Throws(8, 138)(96, 230)Olympic Winningyear throw1908 134.1 ft1912 148.3 ft1920 146.6 ft1924 151.4 ft1928 155.3 ft1932 162.4 ft1936 165.6 ft1948 173.2 ft1952 180.5 ft1956 184.9 ft1960 194.2 ft1964 200.1 ft1968 212.5 ft1972 211.3 ft1976 221.5 ft1980 218.7 ft1984 218.5 ft1988 225.8 ft1992 213.7 ft1996 227.7 ft100008 16 24 32 40 48 56 64 72 80 88 96 xYears since 1900DATA UPDATE ofInformation Please Almanacat www.mcdougallittell.comINTERNETNext, find two points that lie on the line, such as (8, 138) and (96, 230). Find theslope of the line through these points.y 2 º y 1m = = 23 0 º 13896º 8= 9 2 8 ≈ 1.05x2 º x 18To find the y-intercept of the line, substitute the values m = 1.05, x = 8, andy = 138 in the slope-intercept form.y = mx + bWrite slope-intercept form.138 = (1.05)(8) + b Substitute 1.05 for m, 8 for x, and 138 for y.138 = 8.4 + b Simplify.129.6 = b Solve for b. An approximate equation of the best-fitting line is y = 1.05x + 129.6. In mostyears, the winner of the discus throw was able to throw the discus farther thanthe previous winner.294 Chapter 5 Writing Linear Equations