Q. 15 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 11–16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.    

Step-by-Step Solution

Answer

(a). The scatter plot diagram is:

(b). The equation of the line is $10y-40x=1800$.

(c). The graph of the line is 

(d). The equation of the best fit is$y=3.861x+180.3$

(e). The graph of the best fit on the scatter plot is 

Step 1. Given information

We have the given table as below:

Part (a) Step 1. Scatter plot

The scatter plot of the given data is 

Part (b) Step 1. Equation of line

Let us take two points from the scatter plot as

$(-20,100) \mathrm{and} (-10,140)$

Now, the equation of the line is,

$$\begin{gathered} y-100=\frac{140-100}{-10+20}\left(x+20\right) \\ \Rightarrow y-100=\frac{40}{10}\left(x+20\right) \\ \Rightarrow 10y-1000=40x+800 \\ \Rightarrow 10y-40x=1800 \end{gathered}$$

Part (c) Step 1. Graph of the line

Graph of the line found in part (b) on the scatter diagram is as follows.

The equation of the line is $10y-40x=1800$,

Part (d) Step 1. Equation of best fit.

The equation of the best fit is:

$y=3.861x+180.3$

Part (e) Step 1. Graph of best fit.

The graph of the best fit on the scatter plot is as shown below: