Chapter SH, Problem 8.9.3EP

(a)

To determine

To calculate: To write the equation in slope-intercept form for the line of fit for the data

Answer to Problem 8.9.3EP

Equation for the line of fit in slope-intercept form is $y=-0.53x+1084.89$

Explanation of Solution

Given information: In 2003, $23.2\%$ of people between the ages of $65$ and $74$ were working. In 2020, only $19.6\%$ of that age group was working

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Equation of line passing through the points given as

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

Calculation:

In 2003, $23.2\%$ of people between the ages of $65$ and $74$ were working. In 2020, only $19.6\%$ of that age group was working

Let number of people working between the aged of $65$ and $74$ be $y$

Let the year be $x$

Points on the graph as

  $\left(2003,23.3\right)$ and $\left(2010,19.6\right)$

Equation of line passing through the points given as

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

Substituting the values,

  $\begin{array}{l}y-23.3=\frac{23.3-19.6}{2003-2010}\left(x-2003\right)\\ y-23.3=\frac{3.7}{-7}\left(x-2003\right)\\ y-23.3=-0.528\left(x-2003\right)\\ y-23.3=-0.53\left(x-2003\right)\\ y-23.3=-0.53x+1061.59\\ y=-0.53x+1084.89\end{array}$

Conclusion:

Hence, equation for the line of fit for the data is $y=-0.53x+1084.89$

(b)

To determine

To calculate: To predict the percent of that age group that will be working in $2015$

Answer to Problem 8.9.3EP

The percent of that age group that will be working in $2015$ is $16.94\%$

Explanation of Solution

Given information: In 2003, $23.2\%$ of people between the ages of $65$ and $74$ were working. In 2020, only $19.6\%$ of that age group was working

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Equation of line passing through the points given as

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

Calculation:

In 2003, $23.2\%$ of people between the ages of $65$ and $74$ were working. In 2020, only $19.6\%$ of that age group was working

Equation of line of fit for the data is as follows:

  $y=-0.53x+1084.89$

For $x=2015$ , substitute the value in above equation,

  $\begin{array}{l}y=-0.53\left(2015\right)+1084.89\\ y=-1067.95+1084.89\\ y=16.94\end{array}$

Conclusion:

Hence, thepercent of that age group that will be working in $2015$ is $16.94\%$