Chapter 9.7, Problem 38SR

To determine

The equation that relates human age to horse age and find the equivalent horse age for a human who is 16 years old

Answer to Problem 38SR

The equation for 16 years old human is $x=\frac{16}{3}$ .

Explanation of Solution

Given information:

The pair of points, $\left(0,0\right),\left(1,3\right)\text{,}\left(2,6\right)\text{,}\left(3,9\right)\text{,}\left(4,12\right)\text{and }\left(5,15\right)$

  

Concept Used:

The slope of a line connecting the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}\text{Equation}\\ y-y_1=m\left(x-x_1\right)\end{array}$

Calculation:

In order to find the slope of the line passing through the points $\left(1,3\right),\text{ and }\left(2,6\right)$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(1,3\right),\text{ and }\left(x_2,y_2\right)=\left(2,6\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{6-3}{2-1}\\ =\frac{3}{1}\\ =3\end{array}$

And then the equation for 16 years old human

  $\begin{array}{c}y-y_1=m\left(x-x_1\right)\\ 16-3=3\left(x-1\right)\\ 13=3x-3\\ 13+3=3x-3+3\\ 16=3x\\ \frac{16}{3}=\frac{3x}{3}\\ \Rightarrow x=\frac{16}{3}\end{array}$

Thus, the equation for 16 years old human is $x=\frac{16}{3}$ .