Chapter 8.9, Problem 2CYU

(a)

To determine

The slope-intercept form equation for the equation of the line of fit with the help of the following graph:

  

Answer to Problem 2CYU

The final slope intercept form equation is derived as $y=0.4x+0.8$

Explanation of Solution

Given:

  

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where;

Slope: $m$

Y-intercept: $\left(0,b\right)$

Calculation:

Consider,

Year: $x$

Sales: $y$

There are two points are given in the graph:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(4,2.4\right)\\ B=\left(x_2,y_2\right)=\left(5,2.8\right)\end{array}$

Now use any two points to calculate the slope intercept from equation:

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{2.8-2.4}{5-4}=\frac{0.4}{1}=0.4$

Now, the slope intercept form equation is written as:

  $\begin{array}{l}y=mx+b\\ y=0.4x+b\end{array}$

Now put the value of $\left(x_1,y_1\right)=\left(4,2.4\right)$ in the above eq. to get the Y-intercept:

  $\begin{array}{l}y=mx+b\\ 2.4=0.4\left(4\right)+b\\ b=2.4-1.6\\ b=0.8\end{array}$

So, the final slope intercept form equation is:

  $\begin{array}{l}y=mx+b\\ y=0.4x+0.8\end{array}$

Conclusion:

Hence, slope-intercept form is derived with the help of the line of fit.

(b)

To determine

The number of sales of books in the year $16$ with line of fit equation from the first subpart

Answer to Problem 2CYU

There are $7.2$ sales books for year $16$

Explanation of Solution

Given:

  $x=16$

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where;

Slope: $m$

Y-intercept: $\left(0,b\right)$

Calculation:

From the first subpart:

The final slope intercept form equation is derived as:

  $\begin{array}{l}y=mx+b\\ y=0.4x+0.8\end{array}$

Now, to calculate the number of books sales $y$ , need to put $x=16$ in above eq.

  $\begin{array}{l}y=mx+b\\ y=0.4\left(16\right)+0.8\\ y=6.4+0.8\\ y=7.2\end{array}$

So, for the year $x=16$ , there are $y=7.2$ sales for books.

Conclusion:

Hence, sales books in the year $x=16$ is $y=7.2$ .