Q. 16 - 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$10y-3x=190$

(c). Graph of the equation on the scatter plot is 

(d) Equation of the best fit is$y= 0.4421x+23.46$

(e) Graph of the best fit on the scatter plot is

Step 1. Given information

The given table is :

Part (a) Step 1. Scatter plot

The scatter plot of the given data is as shown below:

Part (b) Step 1. Equation of line

Let us take two points from the scatter plot as

$(-30,10) \mathrm{and} (-20,13)$

Now, the equation of line is

$$\begin{gathered} y-10=\frac{13-10}{-20+30}\left(x+30\right) \\ \Rightarrow y-10=\frac{3}{10}\left(x+30\right) \\ \Rightarrow 10y-100=3x+90 \\ \Rightarrow 10y-3x=190 \end{gathered}$$

Part (c) Step 1. Graph of the line

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

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

The equation of the best fit is:

$y=0.4421x + 23.46$

Part (e) Step 1. Graph of best fit

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