1. 7-7 Fitting Equations to Data Warm-up Problems 1.Write the equation of the line with slope –2 and y-intercept 6. 2.Write the slope intercept form of the equation for the line with slope 7 containing the point (3, 8). 3.Write the slope-intercept form of the equation for the line containing the points (9, 2) and (3, 5).

2. Chapter 7 7-7 Fitting Equations to Data

3. Example 1 To produce 50 copies of a school newspaper, the cost per paper is 26 ¢. To produce 200 newspapers, the cost per paper is 20 ¢. Let n be the number of copies of a school newspaper, and let c be the cost per paper. Assume that a linear relationship fits these data with ordered pairs (n, c). 1.Find the linear equation that fits these data. 2.Use the linear equation to predict what it would cost per paper to produce 300 copies.

4. Question: How much would it cost per paper to produce 300 copies? Data: 50 copies cost 26 ¢ each; 200 copies cost 20 ¢ each. 1.Use the ordered pairs (50, 26) and (200, 20) to find the linear equation.

5. 2.To find the cost per paper for 300 papers, substitute 300 for n and solve for c. The cost to produce 300 papers would be 16 ¢ per paper.

6. Example 2 The chart shows the number of daily newspapers published in the United States during the even- numbered years from 1982 to 1996. YearNewspaper 19821711 19841688 19861657 19881642 19901611 19921570 19941548 19961520

7. Let a be the number of years since 1980. (For 1982, for example, a = 2.) Let d be the number of daily newspapers published. Graph the ordered pairs (a, d). Draw a line of best fit and find an equation of the line. Use the line to predict the number of daily newspapers in the year 2000. YearNewspaper 19821711 19841688 19861657 19881642 19901611 19921570 19941548 19961520

8. Try This a.A college record in the 100-m dash in 1960 (t) was 10.5 seconds (r). In 1990 the new record was 10.2 seconds. Assume a linear relationship fits these data with ordered pair (t, r). 1.Find a linear equation to fit the data points. 2.Use the linear equation to predict the record in 2000.

9. Try This b.Graph the ordered pair (d, c). Draw the line of best fit and find the equation of the line. Distance (d) in miles 1015202530405060 Cost (c)1015202224354250