Question

Assume that y varies inversely as x, how do you write an inverse variation equation that relates x and y given y=-1 when x=-12?

Answer 1

`y=12/x`

Explanation:

We know that `ypropto1/x`, and since `y` is proportional to `1/x` we can add a constant, `y=k1/x`.

To find `k` we rearrange to get `k=yx`

We are given `x` and `y`, so we just put our values in to get `k=xy=-12*-1=12`

`y=12*1/x=12/x`

Answer 2

`y-12/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=-1" when "x=-12`

`y=k/xrArrk=yx=-12xx-1=12`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=12/x)color(white)(2/2)|)))`