Chapter 8.5, Problem 27PPS

To determine

To find out the relation is direct or inverse variation, or neither

Answer to Problem 27PPS

The relation show neither.

Explanation of Solution

Given information:

  $\begin{array}{l}{y}_1=4\text{ , }{x}_1=2\\ y_2=9\text{, }{x}_2=3\\ y_3=16\text{, }{x}_3=4\\ y_4=25{\text{, x}}_4=5\end{array}$

The relation can be obtained as

If y varies inversely as x , then

  $\begin{array}{l}y\propto \frac{1}{x}\\ yx=k\left[k=\text{constant}\right]\\ \end{array}$

Put the values of $x_1=2$ , $y_1=4$ in above equation

  $\begin{array}{l}k=4*2\\ k=8\end{array}$

Note that each $\left(x*y\right)\text{ is not equal to 8}$

Again,

If y varies directly as x , then

  $\begin{array}{l}y\propto x\\ k=\frac{y}{x}\left[k=\text{constant}\right]\end{array}$

Put the values of $x_1=2$ , $y_1=4$ in above equation

  $\begin{array}{l}k=\frac{4}{2}\\ k=2\end{array}$

Note that each y is not 2 times more than the value of x

Hence,

The relation show neither.