Q. 11 - 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 the line is  $3x-2y=1$.

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

(d). The line by utility is $y=2.0357x-2.3571$.

(e) The graph best fit line 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

$\left(3,4\right) \mathrm{and} \left(5,7\right)$.

Now, the equation of the line is

$$\begin{gathered} y-4=\frac{7-4}{5-3}\left(x-3\right) \\ \Rightarrow y-4=\frac{3}{2}\left(x-3\right) \\ \Rightarrow 2y-8=3x-9 \\ \Rightarrow 3x-2y=1 \end{gathered}$$

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. Line of best fit

The line of best fit is $y=2.036x-2.357$ and the graph of utility is,

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,