Question

Assume that y varies inversely as x, how do you write an inverse variation equation that relates x and y given y=8 when x=6?

Answer 1

`xy=48` is the inverse variation equation of `x and y`

Explanation:

`y prop 1/x :. y = k*1/x or x*y= k ; k` is constant of

proportionality. `y=8 ; x=6 ; x*y=k :. k = 6*8=48`

`:. x*y=48` is the inverse variation equation of `x and y` [Ans]

Answer 2

`y=48/x`

Explanation:

`"the initial statement is "yprop1/x`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`rArry=kxx1/x=k/x`

`"to find k use the given condition"`

`y=8" when "x=6`

`y=k/xrArrk=yx=8xx6=48`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=48/x)color(white)(2/2)|)))`