A general linear equation is given by:
[tex]y = a*x + b[/tex]
Where a is the slope and b is the y-intercept.
Here we will find that the linear equation that represents the situation is
[tex]y = 0.033*x + 1.269[/tex]
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:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
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:
[tex]a = \frac{1.7 - 1.5}{13 - 7} = 0.033[/tex]
So the linear equation is something like:
[tex]y = 0.033*x + b[/tex]
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:
[tex]1.5 = 0.033*7 + b\\\\1.5 - 0.033*7 = b = 1.269[/tex]
Then the linear equation is:
[tex]y = 0.033*x + 1.269[/tex]
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:
[tex]y = 0.033*48 + 1.269 = 2.853[/tex]
Then the median salary in 2048 will be $2.853 million
If you want to learn more, you can read:
https://brainly.com/question/1189779
