Question

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.

Answer 1

`y=(1)/(30)(x-7)+1.5`

2.8 million is what we get in 2047

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 .2

The 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
`y-1.5=(1)/(30)(x-7)`.

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
`y-y_1=m(x-x_1)`.

So adding 1.5 on both sides of
`y-1.5=(1)/(30)(x-7)` gives me
`y=(1)/(30)(x-7)+1.5`

So now it says what is the medium salary in 2047 I believe. So we are going to plug in 47.

This gives us

`y=(1)/(30)(47-7)+1.5`

`y=(1)/(30)(40)+1.5`

`y=(4)/(3)+1.5`

`y=2.833333333333333333333333`

So 2.8 million