Q. 12 - 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 $y=x-3$.

(c). The graph of the line is,

(d) The best line of fit is $y=1.1285x-3.8619$.

(e). The line of best is 

Step 1. Given information

The given data is:

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 $(3,0) \mathrm{and} (5,2)$

Now, the equation of the line is,

$\begin{array}{rcl}y-y& =& \frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ y-0& =& \frac{2-0}{5-3}\left(x-3\right)\\ y& =& \frac{2}{2}\left(x-3\right)\\ y& =& x - 3\end{array}$

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. Line of best fit

The line of best fit is $y=1.1285x-3.8619$ and the utility graph is defined as,

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

Using a graphing utility the scatter diagram and graph the line of best fit on it is: