Chapter 1.3, Problem 13E

To determine

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 13E

The data show in a linear graph equation of line is $21x-5y=-9$ . For 15 mins walking the calories burned is $\frac{324}{5}$ .

Explanation of Solution

Given Information: The data given as:

Minutes walking, x	1	6	11	13	16
Calories burned, y	6	24	50	56	70

If the graph Is drawn by taking points (1,6) (6,27) (11,50) (13,56) (16,70). It will form a linear graph. This line most closely appears to fit the data.

Now find the slope by taking any two points from the graph (1,6) and (6,27).

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

  $=\frac{27-6}{6-1}$

  $=\frac{21}{5}$

The equation of line

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-6=\frac{21}{5}(x-1)\end{array}$

  $\begin{array}{l}5y-30=21x-21\\ 21x-5y=-30+21\\ 21x-5y=-9\end{array}$

Now put $x=15$

  $\begin{array}{l}21(5)-5y=-9\\ 315-5y=-9\\ -5y=-9-315\\ -5y=-324\\ y=\frac{324}{5}\end{array}$

Thus, for walking of 15 minutes calories burned is $\frac{324}{5}$ .