Question

Suppose y varies inversely with x, how do you write an equation for the inverse variation if y = 8 when x = 1/2?

Answer 1

Since it is an inverse variation it can be represented as:
`color(red)(y) = color(blue)(k/color(red)(x` , where `color(blue)(k` represents the constant term , `color(red)(x and y)` are the variables.

Values for the variables are:
`y=8` and `x=1/2`

substituting these values :
`color(red)(y) = color(blue)(k/color(red)(x`
`color(red)(y.x) = color(blue)(k`

`1/2 . 8 = color(blue)(k)`
we get the constant as `color(blue)k = 4`

`color(red)(y) = color(blue)(4/color(red)(x`

`color(red)(x.y) = color(blue)(4`, represents the inverse variation in which constant is `4`.