Answer:
In 17th year, his income was $30,700.
Step-by-step 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
and
, then the equation of line is
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
The equation of line is
![y-17900=\frac{20300-17900}{4-1}(x-1)](https://tex.z-dn.net/?f=y-17900%3D%5Cfrac%7B20300-17900%7D%7B4-1%7D%28x-1%29)
![y-17900=\frac{2400}{3}(x-1)](https://tex.z-dn.net/?f=y-17900%3D%5Cfrac%7B2400%7D%7B3%7D%28x-1%29)
![y-17900=800(x-1)](https://tex.z-dn.net/?f=y-17900%3D800%28x-1%29)
![y-17900=800x-800](https://tex.z-dn.net/?f=y-17900%3D800x-800)
Add 17900 on both sides.
![y=800x-800+17900](https://tex.z-dn.net/?f=y%3D800x-800%2B17900)
![y=800x+17100](https://tex.z-dn.net/?f=y%3D800x%2B17100)
The income equation is y=800x+17100.
Substitute y=30,700 in the above equation.
![30700=800x+17100](https://tex.z-dn.net/?f=30700%3D800x%2B17100)
Subtract 17100 from both sides.
![30700-17100=800x](https://tex.z-dn.net/?f=30700-17100%3D800x)
![13600=800x](https://tex.z-dn.net/?f=13600%3D800x)
Divide both sides by 800.
![\frac{13600}{800}=x](https://tex.z-dn.net/?f=%5Cfrac%7B13600%7D%7B800%7D%3Dx)
![17=x](https://tex.z-dn.net/?f=17%3Dx)
Therefore, in 17th year his income was $30,700.