Question

Find the variation constant and an equation of variation where y varies inversely as x and y = 12 when x = 9.The variation constant isThe equation of variation is y =

Answer 1

The variation constant is 108

The equation of variation is y = 108/x

Step-by-step explanation

y varies inversely to x implies:

`y\propto(1)/(x)`

So, introducing a constant, we have

`\begin{gathered} y=k.(1)/(x) \\ y=(k)/(x)----a \end{gathered}`

Substitute y = 12 and x = 9 into (a)

`\begin{gathered} 12=(k)/(9) \\ k=12*9 \\ k=108 \end{gathered}`

Therefore the variation constant = 108

To find the equation of variation, substitute k = 108 into (a)

`\begin{gathered} \text{Recall (a)} \\ y=(k)/(x) \\ \therefore\text{ The equation of variation is }y=(108)/(x) \end{gathered}`