Q. 13 - 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 is

(b) The equation of line is $y-x=1$

(c). The graph of the line on the scatter plot is

(d). The equation line of best fit is$y=2.2x+1.2$

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

$(-1,0) \mathrm{and} (0,1)$

Now, the equation of line is

$$\begin{gathered} y-0=\frac{1-0}{0-(-1)}\left(x-(-1)\right) \\ \Rightarrow y=x+1 \\ \Rightarrow y-x=1 \end{gathered}$$

Part (c) Step 1. Graph of the line

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

Equation of line is$y-x=1$.

Part (d) Step 1. Line of best fit

The equation of the best fit line is 

$y=2.2x+1.2$

Part (e) Step 1. Line of best fit diagram

The graph of the best fit line is as follows: