Chapter SH, Problem 8.9.2EP

(a)

To determine

To calculate: To write the equation in slope-intercept form for the line of fit and round to the nearest tenth

Answer to Problem 8.9.2EP

Equation for the line of fit in slope-intercept form is $y=0.7x+10$

Explanation of Solution

Given information: Scatter plot and line of fit showing the number of housing units for the U.S.

  

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:

Scatter plot is given as follows:

  

Points on the graph as

  $\left(2,12.6\right)$ and $\left(7,15\right)$

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,

  $\begin{array}{l}y-15=\frac{15-12.6}{7-2}\left(x-7\right)\\ y-15=\frac{3.6}{5}\left(x-7\right)\\ y-15=0.72\left(x-7\right)\\ y-15=0.72x-5.04\\ y=0.72x+9.96\\ y=0.7x+10\end{array}$

Conclusion:

Hence, equation for the line of fit is $y=0.7x+10$

(b)

To determine

To calculate: To estimate the number of housing units in $2020$

Answer to Problem 8.9.2EP

The number of housing units in $2020$ is $22.6$ millionss

Explanation of Solution

Given information: Scatter plot and line of fit showing the number of housing units for the U.S.

  

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:

Scatter plot is given as follows:

  

Equation for the line of fit is $y=0.7x+10$

For year $2020$

Here, Base year, $0=1998$

Thus, for $2020$ , $x=18$

Substituting the values in above equation,

  $\begin{array}{l}y=0.7\left(18\right)+10\\ y=12.6+10\\ y=22.6\end{array}$

Conclusion:

Hence, number of housing units in $2020$ is $22.6$ millions