Chapter 8, Problem 17CT

a.

To determine

To make:

A scatter plot of the data points and draw a line that appears to best fit the data points.

Answer to Problem 17CT

Our required graph would look like:

  

Explanation of Solution

Given:

The table shows the number of televisions sold each month at a retail store.

  

Calculation:

Upon plotting our given data points and drawing a line of best fit, we will get our required graph as shown below:

  

b.

To determine

To write:

An equation of our line in slope-intercept form.

Answer to Problem 17CT

The equation of our line in slope-intercept form would be $y=9x+357$ .

Explanation of Solution

Given:

The table shows the number of televisions sold each month at a retail store.

  

Calculation:

First of all, we will find slope of line passing through points $(2,375)\text{and }(5,402)$ as shown below:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{402-375}{5-2}\\ m=\frac{27}{3}\\ m=9\end{array}$

Now we will substitute slope and coordinates of point $(2,375)$ in point-slope form as:

  $\begin{array}{l}y-375=9\left(x-2\right)\\ y-375=9x-18\\ y-375+375=9x-18+375\\ y=9x+357\end{array}$

Therefore, the equation of our line in slope-intercept form would be $y=9x+357$ .

c.

To determine

To predict:

The number of televisions sold at the store during the 7^th month.

Answer to Problem 17CT

There were 420 televisions sold at the store during the 7^th month.

Explanation of Solution

Given:

The table shows the number of televisions sold each month at a retail store.

  

Calculation:

To predict the number of televisions sold during 7th month, we will substitute $x=7$ in line of best fit as:

  $\begin{array}{l}y=9x+357\left(\text{Line of best fit}\right)\\ y=9(7)+357\left(\text{Substituting }x=7\right)\\ y=63+357\\ y=420\end{array}$

Therefore, there were 420 televisions sold at the store during the 7^th month.