Question

How do you write an inverse variation equation given y=-1 when x=-12?

Answer 1

`color(green)(x * y =12)`

Explanation:

If `x` and `y` form an inverse variation then
`color(white)("XXX")x * y = k` for some constant `k`

Given that `(x=-12,y=-1)` is a solution to the required relation:
`color(white)("XXX")(-12) * (-1) = k`

`rArr k=12`

Answer 2

`y = 12/x`

Explanation:

In an inverse variation - or inverse proportion, as one quantity increases the other decreases.

This can be written as: `y prop1/x`

Variations (proportions) are linked by a constant (k)

We can write a variation as an equation by using the constant.

`y = k/x`

`x xx y = k" "larr`now we can find a value for `k` using the values of `x and y` which were given

`k = -12 xx-1 = 12`

The equation is therefore: `y = 12/x`

This is the equation for a hyperbola which is the graph of inverse proportion.