Question

A.) The median player salary for the New York Yankees was $1.5 million in 2007 and $1.7 million in 2013. Write a linear equation giving the median salary y in terms of the year x. (Let y be in millions of dollars and let
x = 7
represent 2007.)

b.) Use the equation to predict the median salary in 2048. (Round your answer to one decimal place.)
$ million

Answer 1

A general linear equation is given by:

$y = a*x + b$

Where a is the slope and b is the y-intercept.

Here we will find that the linear equation that represents the situation is

$y = 0.033*x + 1.269$

And we can expect that the median salary in 2048 is $2.853 million

If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

Here we know that:

in 2007 (x = 7) the median player salary was y = $1.5 million

in 2013 (x = 13) the median player salary was y = $1.7 million.

Then we have two points that we can write as:

(7, 1.5)

(13, 1.7)

Note that the y-value is in millions.

Then the slope of the linear equation will be:

$a = \frac{1.7 - 1.5}{13 - 7} = 0.033$

So the linear equation is something like:

$y = 0.033*x + b$

To find the value of b, remember the point (7, 1.5), this means that when we have x = 7, we also have y = 1.5, then we can replace these in the above equation:

$1.5 = 0.033*7 + b\\\\1.5 - 0.033*7 = b = 1.269$

Then the linear equation is:

$y = 0.033*x + 1.269$

b) Now we want to predict the median salary in 2048. For 2048 the x-value is x = 48

So we just need to evaluate this in the linear equation:

$y = 0.033*48 + 1.269 = 2.853$

Then the median salary in 2048 will be $2.853 million

If you want to learn more, you can read:

brainly.com/question/1189779