2. Vocabulary The line that most closely follows a trend in data. Best-fitting line 1.8Predict with Linear Models Use of a line or its equation to approximate a value between two known values. Linear Interpolation Use of a line or its equation to approximate a value outside the range of two known values. Linear Extrapolation A zero of a function y = f (x) is an x- value for which f (x) = 0 (or y = 0). Zero of a Function

3. Interpolate using an equation Salaries The table shows a company’s annual salary expenditure (in thousands of dollars) from 200 to 2004. Example 1 1.8Predict with Linear Models Year Annual Salary of Expenditure a.Make a scatter plot of the data. Enter the data into lists on a graphing calculator. (Stat – Edit) Make a scatter plot, letting the number of years since 2000 be the ___________ (0, 2, 3, 4) and the annual salary expenditure be the _______________. x-values y-values To graph (2 nd Stat Plot – enter – enter – Zoom 9)

4. Interpolate using an equation Salaries The table shows a company’s annual salary expenditure (in thousands of dollars) from 200 to 2004. Example 1 1.8Predict with Linear Models Year Annual Salary of Expenditure b.Find an equation that models the annual salary expenditure (in thousands of dollars) as a function of the number of years since 2000. Use a calculator the find the best-fitting line. (Stat – Calc) The equation of the best-fitting line is ____________________. (Stat – right arrow - #4 – enter )

5. Interpolate using an equation Salaries The table shows a company’s annual salary expenditure (in thousands of dollars) from 200 to 2004. Example 1 1.8Predict with Linear Models Year Annual Salary of Expenditure c.Approximate the annual salary expenditure in 2001. Graph the best-fitting line. Use the trace feature and the arrow keys to find the value of the equation when x = ____. (type in equation using y = key then hit GRAPH) The annual salary expenditure in 2001 was _______ thousand dollars.

6. Extrapolate using an equation Salaries Look back to example 1. Example 2 1.8Predict with Linear Models Year Annual Salary of Expenditure a.Use the equation from example 1 to approximate the annual total salary expenditure in 2005 and 2006. Evaluate the equation of the best-fitting line from Example 1 for x = ____ and x = _____. The model predicts the average annual salary expenditure as ______ thousand dollars in 2005 and _______ thousand dollars in 2006.

7. Extrapolate using an equation Salaries Look back to example 1. Example 2 1.8Predict with Linear Models Year Annual Salary of Expenditure b.In 2005, the annual total salary expenditure was actually 1180 thousand dollars. In 2006, the annual total salary expenditure was actually 1259 thousand dollars. Describe the accuracy of the extrapolations made in part (a). The difference between the predicted annual salary expenditure and the actual annual salary expenditure in 2005 and 2006 are ____ thousand dollars and _____ thousand dollars, respectively. The difference in actual and predicted annual salary expenditures increased from 2005 to 2006. So, the equation of the best-fitting line gives a less accurate prediction for years farther from the given data.

8. Checkpoint. Complete the following exercise. 1.Population The table shows the population of a town from 2002 to 2006. 1.8Predict with Linear Models Year Population Find an equation that models the population as a function of the number of years since 2002. Approximate the population in 2003, 2007, and 2008.

9. Find the zero of a function Public Transit The percentage y of people in the U.S. that use public transit to commute to work can be modeled by the function y =  0.045x + 5.7 where x is the number of years since 1983. Find the zero of the function to the nearest whole number. Explain what the zero means in this situation. Example 3 1.8Predict with Linear Models Substitute ____ for y in the model and solve for x. Write original function. Substitute ____ for y. Solve for x. The zero of the function is about ____. According to the model, there will be no people who use public transit to commute to work _____ years after _____, or in _____.

10. Checkpoint. Complete the following exercise. 2.Profit The profit p of a company can be modeled by p = 300 – 3t where t is the number of years since 2000. Find the zero of the function. 1.8Predict with Linear Models Explain what the zero means in this situation. There will be no profit in 2100

11. 1.8Predict with Linear Models