Question

This relation is an inverse variation. {(–1, 8), (4, –2), (–2, 4)} Which equation represents this relation?

Answer 1

`y = -(8)/(x)`

Explanation:

Given

Inverse Variation:

`Points: \{(-1, 8), (4, -2), (-2, 4)\}`

Required

Determine the equation of the relation

An inverse relation is represented as:

`y = (k)/(x)`

Where k = constant of variation

Make k the subject:

`k = xy`

When x = -1, y = 8

So, we have:

`k = -1 * 8`

`k = -8`

When x = 4, y = -2

`k = 4 * -2`

`k = -8`

When x = -2, y = 4

`k= -2 * 4`

`k = -8`

From above calculations, we've established that:

`k = -8`

Substitute -8 for k in
`y = (k)/(x)`

`y = (-8)/(x)`

`y = -(8)/(x)`

Hence, the equation is:

`y = -(8)/(x)`