Chapter 4.4, Problem 8PPS

(a)

To determine

To write: the slope intercept form of an equation for the line of fit.

Answer to Problem 8PPS

  $y=-\frac{3}{8}x+22.5$

Explanation of Solution

Given information:

The scatter plot of gallons of milk consumption per person for selected years

Use the points $\left(2,21.75\right)$ and $\left(4,21\right)$ .

  

Calculation:

Slope intercepts form of a line $y=mx+b$

Now, calculate $m_1$ ,

  $\begin{array}{c}{m}_1=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{21-21.75}{4-2}\\ =-\frac{0.75}{2}\\ =-\frac{3}{8}\end{array}$

Slope intercept form of a line $y=mx+b$

  $y=-\frac{3}{8}x+b$

Plugging the point $\left(4,21\right)$

  $\begin{array}{c}21=-\frac{3}{8}\left(4\right)+b\\ 21=-\frac{3}{2}+b\\ b=21+1.5\\ b=22.5\end{array}$

So, $y=-\frac{3}{8}x+22.5$

(b)

To determine

To predict: the milk consumption in 2005.

Answer to Problem 8PPS

The consumption of milk in 2025 is 13.125gallons.

Explanation of Solution

Given information:

The scatter plot of gallons of milk consumption per person for selected years

Use the points $\left(2,21.75\right)$ and $\left(4,21\right)$ .

  

Calculation:

For the year 2025 the corresponding value of $x=25$ .

Plugging the above equation

  $\begin{array}{c}y=-\frac{3}{8}\left(25\right)+22.5\\ y=13.125\end{array}$

(c)

To determine

To predict: the year which milk consumption will be 10 gallons.

Answer to Problem 8PPS

The years will be $2033\frac{1}{3}$ .

Explanation of Solution

Given information:

The scatter plot of gallons of milk consumption per person for selected years

Use the points $\left(2,21.75\right)$ and $\left(4,21\right)$ .

  

Calculation:

Consider the equation,

  $y=-\frac{3}{8}x+22.5$

Plugging the value of $y$ as 10

  $10=-\frac{3}{8}x+22.5$

Subtracting 22.5 on both sides,

  $\begin{array}{c}10-22.5=-\frac{3}{8}x+22.5-22.5\\ -12.5=-\frac{3}{8}x\\ x=\frac{12.5}{0.375}\\ x=33\frac{1}{3}\end{array}$

So, the year will be

  $2000+33\frac{1}{3}=2033\frac{1}{3}$ years.

(d)

To determine

To estimate: the consumption of milk for any year using the equation.

Answer to Problem 8PPS

Yes it is reasonable to use the equation to find the consumption milk in any year because the graph is almost linear

Explanation of Solution

Given information:

The scatter plot of gallons of milk consumption per person for selected years

Use the points $\left(2,21.75\right)$ and $\left(4,21\right)$ .

  

Calculation:

Yes it is reasonable to use the equation to find the consumption milk in any year because the graph is almost linear.