Question

Xy - 11= 5

y/x = 5
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^^^
fraction

Tell whether x and y show direct variation. Explain your reasoning.

Answer 1

An equation shows inverse variation if it can be represented in the form
`y = (k)/(x)`. The first equation can be rearranged into this form:


`xy - 11 = 5`

`xy = 16`

`y = (16)/(x)`

This is in the form
`y = (k)/(x)`, so the first equation shows inverse variation.

An equation shows direct variation if it can be represented in the form
`y = kx`. The second equation can be rearranged into this form:


`(y)/(x) = 5`

`y = 5x`

This is in the form
`y = kx`, so the second equation shows direct variation.