Chapter 11.6, Problem 1P

To determine

Equation for the inverse variation.

Answer to Problem 1P

  $y=\frac{54}{x}$

Explanation of Solution

Given Information:

The variable y varies inversely with x. The value of y is 9 when x is 6.

Calculation:

Given that the variable y varies inversely with x. So we have

  $\begin{array}{l}y\propto \frac{1}{x}\\ y=\frac{k}{x}\\ yx=k\mathrm{.......}\left(i\right)\end{array}$

Here k is the constant of proportionality.

Also given that the value of y is 9 when x is 6. So, on substituting values of x and y in above equation (i), we get

  $\begin{array}{c}yx=k\\ 9\cdot 6=k\\ 54=k\\ k=54\end{array}$

So, with this value of k , above equation (i) becomes

  $\begin{array}{c}yx=54\\ y=\frac{54}{x}\end{array}$