Write a linear equation giving the median salary y in terms of the year x. Then, use the equation to predict the median salary in 2047.

Accepted Solution

Answer:[tex]y=\frac{1}{30}(x-7)+1.5[/tex]2.8 million is what we get in 2047Step-by-step explanation:Ok I see the following given in 2007, the medium salary is 1.5 million and in 2013 the medium salary is 1.7 million.It says let x=7 represent 2007 so that means x=13 would represent 2013.It also says y is in millions so y=1.5 means 1.5 million and y=1.7 means 1.7 million.So we have these points that we need to find a line for:  (7,1.5) and (13,1.7).The slope can be found by using the slope formula given two points.  This looks like this (y2-y1)/(x2-x1).I like to line the points up and subtract then put 2nd difference over 1st difference. Let's do that. (13, 1.7)-(7, 1.5)-----------6       .2The slope is .2/6 or 2/60 (after multiplying top and bottom by 10) or 1/30 (after dividing top and bottom by 2)So point slope form for this line is [tex]y-1.5=\frac{1}{30}(x-7)[/tex].To get the point slope form for this line I just entered my m (the slope) and point (x1,y1) I knew on the line (like (7,1.5) ). Point slope form is [tex]y-y_1=m(x-x_1)[/tex].So adding 1.5 on both sides of  [tex]y-1.5=\frac{1}{30}(x-7)[/tex] gives me  [tex]y=\frac{1}{30}(x-7)+1.5[/tex]So now it says what is the medium salary in 2047 I believe. So we are going to plug in 47.This gives us [tex]y=\frac{1}{30}(47-7)+1.5[/tex][tex]y=\frac{1}{30}(40)+1.5[/tex][tex]y=\frac{4}{3}+1.5[/tex][tex]y=2.833333333333333333333333[/tex]So 2.8 million