Question

​Joe's annual income has been increasing each year by the same dollar amount. The first year his income was ​$17 comma 90017,900​, and the 44th year his income was ​$20 comma 30020,300. In which year was his income $ 30 comma 700 question mark

Answer 1

In 17th year, his income was $30,700.

Explanation:

It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.

Income in first year = $17,900

Income in 4th year = $20,300

Let y be the income at x year.

It means the line passes through the point (1,17900) and (4,20300).

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of line is

`y-17900=(20300-17900)/(4-1)(x-1)`

`y-17900=(2400)/(3)(x-1)`

`y-17900=800(x-1)`

`y-17900=800x-800`

Add 17900 on both sides.

`y=800x-800+17900`

`y=800x+17100`

The income equation is y=800x+17100.

Substitute y=30,700 in the above equation.

`30700=800x+17100`

Subtract 17100 from both sides.

`30700-17100=800x`

`13600=800x`

Divide both sides by 800.

`(13600)/(800)=x`

`17=x`

Therefore, in 17th year his income was $30,700.