Question

Write and graph the inverse variation in which y = 4 when x = 2.

Answer 1

An inverse variation is the one in which the product of x and y is a constant:

`xy=k`

We can find the value of this constant by replace x and y for the given values:

`\begin{gathered} (2)(4)=k \\ k=8 \end{gathered}`

Now, replace k in the initial equation and then solve for y:

`\begin{gathered} xy=8 \\ y=(8)/(x) \end{gathered}`

It means that the relationship is:

`y=(8)/(x)`

The graph of this relationship is: