The table lists data regarding the average salaries of several professional athletes in the years 1991and 2001 year salary

A) use the data points to find a linear function that fits the data B) use the function to predict the average salary in 2005 and 2010 1991 $257000
2001 $ 1440,000
sx=

To find the linear function that fits the data, we need to calculate the slope (s) and the y-intercept (x) of the linear equation.

First, we calculate the change in salary (Δy) and change in years (Δx) between 1991 and 2001:

Δy = 1440000 - 257000 = $1183000
Δx = 2001 - 1991 = 10 years

Next, we calculate the slope (s) using the formula s = Δy/Δx:

s = 1183000/10 = $118300

To find the y-intercept (x), we can substitute one of the given data points into the equation y = mx + c and solve for c. We'll use the data from 1991, with x = 1991 and y = 257000:

257000 = 118300 * 1991 + c
257000 = 235177300 + c
c = 257000 - 235177300
c = -234920300

Therefore, the linear function that fits the data is:

y = 118300x - 234920300

Now, let's use this function to predict the average salaries in 2005 and 2010.

For 2005:
x = 2005
y = 118300 * 2005 - 234920300
y = 236070000 - 234920300
y = $1,149,700

For 2010:
x = 2010
y = 118300 * 2010 - 234920300
y = 237663000 - 234920300
y = $2,742,700

Therefore, the predicted average salary in 2005 is $1,149,700, and in 2010 is $2,742,700.

In order to find a linear function that fits the given data points, we need to calculate the slope and intercept of the line. To do this, we will use the formula for the slope of a line:

slope (m) = (change in y)/(change in x)

To calculate the change in y, we subtract the y-values of the two data points (2001 - 1991):

change in y = 1440000 - 257000 = 1183000

To calculate the change in x, we subtract the x-values of the two data points:

change in x = 2001 - 1991 = 10

Next, we can substitute these values into the slope formula:

slope (m) = 1183000/10 = 118300

Now, we can calculate the intercept (b) using the formula:

intercept (b) = y - mx

Choose one of the data points, let's use the first one, (1991, $257000):

intercept (b) = 257000 - (118300 * 1991) = -234616300

So, the linear function that fits the data is:

f(x) = 118300x - 234616300

To predict the average salary in 2005 and 2010, we can substitute the respective x-values into the linear function:

For 2005 (x = 2005):

f(2005) = 118300 * 2005 - 234616300

For 2010 (x = 2010):

f(2010) = 118300 * 2010 - 234616300

By substituting these values into the equation, you can find the predicted average salaries for 2005 and 2010.