Chapter 1.1, Problem 42E

To determine

To Find:Linear equation giving the median household income ?? in terms of the year ?? and then use the equation to predict the median household income in2021.

Answer to Problem 42E

Linear equation giving the median household income ?? in terms of the year ?? is

  $y=1340x-2643823$ and value of household income in $2021$ is $\$64317$ .

Explanation of Solution

Given:Median household income in United States was $56,277 in 2015 and $57,617 in2016.

Formula used: Equation of line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

  $y-y_1=\left(\frac{y_2- y_1}{x_2- x_1}\right)\left(x-x_1\right)$

Calculation:We have given when $x=2015, y=56,277$ and $x=2016, y=57,617$.

So the corresponding points are $(x_1, y_1)=\left(2015, 56277\right)$ and $\left(x_2, y_2\right)=\left(2016, 57617\right)$.

Equation of line passing through $\left(x_1, y_1\right)$ and $\left(x_2,y_2\right),$

  $y-y_1=\left(\frac{y_2- y_1}{x_2- x_1}\right)\left(x-x_1\right)$

  $y-56277=\left(\frac{57617- 56277}{2016-2015}\right)\left(x-2015\right)$

  $y-56277=1340\left(x-2015\right)$

  $y=1340x-2643823$

The value median household income in 2021 is given by,

  $y=1340\left(2021\right)-2643823$

  $y=64317$

Conclusion:

Therefore,Linear equation giving the median household income ?? in terms of the year ?? is

  $y=1340x-2643823$ and value of household income in $2021$ is $\$64317$ .