Question

If y varies inversely as x, how do you find the constant of variation if y=14 when x=8?

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=14` and `x=8`

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

`(14).(8)= color(blue)(k)`
we get the constant as `color(blue)k = 112`

`color(red)(y) = color(blue)(112/color(red)(x`

`color(red)(x.y) = color(blue)(112`, represents the inverse variation in which constant is `112`.