Chapter 3.2, Problem 11AYU

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.

To determine

To calculate:

1. The scatter diagram of the given data.
2. Find the equation of a line containing 2 points in the scatter diagram.
3. Graph the line found in (b).
4. Find the line of best fit using a graphing utility.
5. Draw the scatter diagram and the line of best fit using a graphing utility.

Answer to Problem 11AYU

Solution:

a.

b. The equation of the line joining the points $\left(3,4\right)$ and $\left(9,16\right)$ is

$y=2x-2$

c.

d. $y=2.035x-2.357$

e.

Explanation of Solution

Given:

The given data is

Formula used:

The point slope form of the equation of the line with points $(x_1,y_1),(x_2,y_2)$ is

$y-y_1=m(x-x_1)$, where $m=\frac{y_2-y_1}{x_2-x_1}$.

Calculation:

a. The scatter diagram of the given data is

b.

Consider the points $\left(3,4\right)$ and $\left(9,16\right)$.

Here, we have

$(x_1,y_1)=(3,4)$

$(x_2,y_2)=(9,16)$

Therefore, on substituting these in the point slope form of the equation of a line, we get

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{16-4}{9-3}=2$

Therefore,

$y-y_1=m(x-x_1)$

$\Rightarrow y-4=2(x-3)$

$\Rightarrow y=2x-6+4$

$\Rightarrow y=2x-2$

Thus, the equation of the line joining the points $(3,4)$ and $\left(9,16\right)$ is

$y=2x-2$

c. The graph of the above line is

d. Using a graphing utility, we can find the line of best fit to be

$y=2.035x-2.357$

e. The line of best fit and the scatter diagram is