Chapter 8, Problem 48SGR

a.

To determine

A scatter plot and line of fit for the following table data:

Year	Ticket cost ($)
$\text{'}03$	$45$
$\text{'}04$	$48$
$\text{'}05$	$56$
$\text{'}06$	$60$
$\text{'}07$	$65$
$\text{'}08$	$80$

Answer to Problem 48SGR

Explanation of Solution

Given:

Year	Ticket cost ($)
$\text{'}03$	$45$
$\text{'}04$	$48$
$\text{'}05$	$56$
$\text{'}06$	$60$
$\text{'}07$	$65$
$\text{'}08$	$80$

Concept Used:

The slope intercept form is:

  $y=mx+b$

Where,

Slope: $m$

  $y$ -intercept: $b$

Calculation:

Consider;

Year: $x$

Cost of ticket: $y$

Now, take the data points as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(03,45\right)\\ B=\left(x_2,y_2\right)=\left(04,48\right)\\ C=\left(x_3,y_3\right)=\left(05,56\right)\\ D=\left(x_4,y_4\right)=\left(06,60\right)\\ E=\left(x_5,y_5\right)=\left(07,65\right)\\ E=\left(x_6,y_6\right)=\left(08,80\right)\end{array}$

Now, the slope is calculated as:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{48-45}{04-03}\\ m=\frac{3}{1}\\ m=3\end{array}$

So, the slope intercept eq. can be written as:

  $\begin{array}{l}y=mx+b\\ y=3x+b\end{array}$

Now, need to put $\left(04,48\right)$ in $y=3x+b$ :

  $\begin{array}{l}y=3x+b\\ 48=3\times 4+b\\ b=48-12\\ b=36\end{array}$

So, the final slope-intercept form is written as:

  $\begin{array}{l}y=3x+b\\ y=3x+36\end{array}$

Now, the scatter plot of the data points and its line of fit eq. is drawn as:

Conclusion:

Hence, the scatter plot and the line of fit is drawn as above.

b.

To determine

The average price value of the concert ticket in the year $2015$

Answer to Problem 48SGR

The average price value of the concert ticket in the year $2015$ is $\$6081$

Explanation of Solution

Given:

  $x=2015$

Concept Used:

The slope intercept form is:

  $y=mx+b$

Where,

Slope: $m$

  $y$ -intercept: $b$

Calculation:

Consider;

Year: $x$

Cost of ticket: $y$

The slope-intercept form is taken from above SUB-PART:

  $\begin{array}{l}y=3x+b\\ y=3x+36\end{array}$

Put the value of the week $x=2015$

  $\begin{array}{l}y=3x+b\\ y=3x+36\\ y=3\times 2015+36\\ y=6045+36\\ y=6081\end{array}$

So the average price of concert ticket in the year $2015$ is $6081$

Conclusion:

Hence, the average price of concert ticket in the year $2015$ is $\$6081$