Chapter 8.9, Problem 5PPS

(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 5PPS

The final slope intercept form equation is derived as $y=\frac{1.3}{3}x+11.76$ .

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 since $1998$ : $x$

Amount spent: $y$

There are two points are given in the graph:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(4,13.5\right)\\ B=\left(x_2,y_2\right)=\left(7,14.8\right)\end{array}$

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

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{14.8-13.5}{7-4}=\frac{1.3}{3}$

Now, the slope intercept form equation is written as:

  $\begin{array}{l}y=mx+b\\ y=\frac{1.3}{3}x+b\end{array}$

Now put the value of $\left(x_1,y_1\right)=\left(4,13.5\right)$ in the above eq. to get the Y-intercept:

  $\begin{array}{l}y=mx+b\\ 13.5=\frac{1.3}{3}\left(4\right)+b\\ b=13.5-1.733\\ b=11.76\end{array}$

So, the final slope intercept form equation is:

  $\begin{array}{l}y=mx+b\\ y=\frac{1.3}{3}x+11.76\end{array}$

Conclusion:

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

(b)

To determine

The amount which will be spend by the government for space and other technology the in the year $2016$ with line of fit equation from the first subpart

Answer to Problem 5PPS

The amount which will be spend by the government for space and other technology for year $2016$ is $885.367billions$

Explanation of Solution

Given:

  $x=2016$

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:

  $\begin{array}{l}y=mx+b\\ y=\frac{1.3}{3}x+11.76\end{array}$

Now, to calculate the amount which will be spending by the government for space and other technology $y$ , need to put $x=2016$ in above eq.

  $\begin{array}{l}y=mx+b\\ y=\frac{1.3}{3}\left(2016\right)+11.76\\ y=873.6+11.76\\ y=885.367\end{array}$

So, for the year $2016$ , the amount which will be spending by the government for space and other technology is $y=\$885.367$

Conclusion:

Hence, spending amount is calculated as $y=\$885.367$