Predict with Linear Models 1.8 Predict with Linear Models Vocabulary The line that most closely follows a trend in data. Best-fitting line 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 Zero of a Function A zero of a function y = f (x) is an x-value for which f (x) = 0 (or y = 0).

Predict with Linear Models 1.8 Predict with Linear Models Interpolate using an equation Salaries The table shows a company’s annual salary expenditure (in thousands of dollars) from 200 to 2004. Example 1 Year Annual Salary of Expenditure 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 (2nd Stat Plot – enter – enter – Zoom 9)

Predict with Linear Models 1.8 Predict with Linear Models Interpolate using an equation Salaries The table shows a company’s annual salary expenditure (in thousands of dollars) from 200 to 2004. Example 1 Year Annual Salary of Expenditure 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) (Stat – right arrow - #4 – enter ) The equation of the best-fitting line is ____________________.

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

Predict with Linear Models 1.8 Predict with Linear Models Extrapolate using an equation Example 2 Salaries Look back to example 1. Year Annual Salary of Expenditure 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.

Predict with Linear Models 1.8 Predict with Linear Models Extrapolate using an equation Example 2 Salaries Look back to example 1. Year Annual Salary of Expenditure 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.

Predict with Linear Models 1.8 Predict with Linear Models Checkpoint. Complete the following exercise. Population The table shows the population of a town from 2002 to 2006. 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.

Predict with Linear Models 1.8 Predict with Linear Models Find the zero of a function Example 3 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. 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 _____.

Predict with Linear Models 1.8 Predict with Linear Models Checkpoint. Complete the following exercise. 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. Explain what the zero means in this situation. There will be no profit in 2100

Predict with Linear Models 1.8 Predict with Linear Models