Chapter 8.1, Problem 4OE

To determine

To state whether the function is a direct variation or not and give the constant of variation.

Answer to Problem 4OE

The function is a direct variation and the constant of variation is $0.5$ .

Explanation of Solution

Given information:

The given ordered pairs of a function are:

  

Calculation :

In the given function, the ratio of $d:t$ is same and can be shown by:

  $\begin{array}{l}\frac{d_1}{t_1}=\frac{d_2}{t_2}=\frac{d_3}{t_3}\\ \frac{\frac{3}{4}}{\frac{3}{2}}=\frac{3}{6}=\frac{\frac{16}{3}}{\frac{32}{3}}\\ \left(\frac{3}{4}\times \frac{2}{3}\right)=\frac{3}{6}=\left(\frac{16}{3}\times \frac{3}{32}\right)=0.5\end{array}$

Hence, the function is a direct variation and the constant of variation is $0.5$ .