Question

Why is `\frac{4}{x}=y` not a direct variation equation?

Answer 1

When you have a direct variation between two variables, this means that as one variable goes smaller, the other variable also goes smaller. When one variable goes larger, the other variable also goes larger.

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Now, let's examine what happens in the equation `4/x = y`

`x = 1`

`=> 4/1 = y`
`=> 4 = y`

`x= 2`

`=> 4/2 = y`
`=> 2 = y`

`x = 10`

`=> 4/10 = y`
`=> 0.4 = y`

Notice as we increase `x` from `1` to `10`, `y` got smaller.
Looking from another perpective, as we decrease `x` from `10` to `1`, `y` got larger.

This means that your equation is an inverse variation