Question

Suppose y varies inversely with x. How do you write an equation for the inverse variation for Y = 5 when x = -5?

Answer 1

`" "y=(-25)/x`

Explanation:

As `x` increases the `y` decreases.

`=> y->1/x" "`

`1/x` becomes smaller as `x` becomes bigger.

To complete this picture we need a constant

Let the constant be `k`

Then

`y" "=" "kxx1/x" " =" " k/x`

We are told that when `y=5" ; "x=-5`

So we have

`y=k/x" " ->" " 5=k/(-5)`

So `k=(+5)xx(-5) = -25`

Thus the equation becomes:`" "y=(-25)/x`