Chapter 1.1, Problem 33E

To determine

Calculate the median salary in $2020$ and also find the linear equation giving the median salary y in terms of x.

Answer to Problem 33E

The median salary in 2020 is $1.93$ million and the linear equation for the median salary is $y=\frac{1}{30}x-\frac{1962}{30}$ .

Explanation of Solution

Given:

It is given in the question that the median player salary for the year $2007$ is $\$1.5$ million and in $2013$ is $\$1.7$ million.

Concept Used:

In this , use the concept of slope equation,point slope form and slope intersept form,and the formula used is $m=\frac{y_2-y_1}{x_2-x_1},y-y_1=m(x-x_1),y=mx+b$ .

Calculation: Now ,it is given that , $(x_1,y_1)=(2007,1.5)$$(x_2,y_2)=(2013,1.7)$

Slope of the line, $m=\frac{y_2-y_1}{x_2-x_1}=\frac{1.7-1.5}{2013-2007}=\frac{0.2}{6}=\frac{1}{30}$

Now , use the point slope form,to get the equation

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-1.5=\frac{1}{30}(x-2007)\\ y=\frac{1}{30}x-\frac{2007}{30}+1.5\\ y=\frac{1}{30}x-\frac{2007}{30}+\frac{45}{30}\\ y=\frac{1}{30}x-\frac{1962}{30}\end{array}$

Now put $x=2020$ ,so we get the salary

  $\begin{array}{l}y=\frac{1}{30}\cdot 2020-\frac{1962}{30}\\ y=\frac{58}{30}\approx 1.93(million\$)\end{array}$

Conclusion:

The salary is $1.93$ million and the equation is $y=\frac{1}{30}x-\frac{1962}{30}$ .