Chapter 1.3, Problem 14E

To determine

To find: The equation of a line of fit. Estimate y when $x=15$ and explain its meaning in the context of the situation.

Answer to Problem 14E

The data show a linear relationship. Equation of line is $x-2y=3$ . Length of hair is 6 in after 15 months.

Explanation of Solution

Given Information: The data is given as:

Minutes walking, x	9	13	18	22	23
Hair length, y	3	5	7	10	11

If draw the graph by taking points (9,3), (13,5), (18,7), (22,10), (23,11). We will find a linear graph. The data shows a linear relationship.

Now find the slope of line by taking any two points from the graph (9,3) and (13,5).

Slope $=\frac{y_2-y_1}{x_2-x_1}$

  $=\frac{5-3}{13-9}$

  $=\frac{2}{4}=\frac{1}{2}$

Now equation of line using point slope from

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-3=\frac{1}{2}(x-9)\end{array}$

  $\begin{array}{l}2y-6=x-9\\ x-2y=-6+9\\ x-y=3\end{array}$

Now put $x=15$

  $\begin{array}{l}15-2y=3\\ -2y=3-15\\ -2y=-12\\ y=6\end{array}$

Thus, the length of hair will be 6 inches after 15 months.