Chapter 1.3, Problem 15E

To determine

To find: Whether the data show a linear relationship. If so, write an equation of a line of fit. Estimate y when $x=15$ and explain its meaning in the context of the situation.

Answer to Problem 15E

The data show a linear relationship. Equation of line is $50x+11y=1000$ . After 15 hours battery life is 22.72%

Explanation of Solution

Given Information: The data is given as:

Minutes walking, x	3	7	9	17	20
Battery life (%), y	86	61	50	26	0

If the graph by taking points (3,86), (7,61), (9,50), (17,26), (20,0). 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 (20,0) and (9,50).

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

  $=\frac{50-0}{9-20}$

  $=\frac{50}{-11}=\frac{-50}{11}$

Now equation of line using point slope from

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-0=\frac{-50}{11}(x-20)\end{array}$

  $\begin{array}{l}y=\frac{-50}{11}(x-20)\\ 11y=-50x+1000\\ 50x+11y=1000\end{array}$

Now put $x=15$

  $\begin{array}{l}50(15)+11y=1000\\ 750+11y=1000\\ 11y=1000-750\\ 11y=250\\ y=\frac{250}{11}\\ y=22.72\end{array}$

Thus, it means after 15 hours battery life will be 22.72%.