Question

How do you tell whether the equation x + 2y = 4 represents a direct variation. If so identify the constant?

Answer 1

`x+2y=4` is not a direct variation

Explanation:

Consider one possible simple solution for `x+2y=4`
`color(white)("XXX")x=2` and `y=1`

If the equation were a direct variation
multiplying `x` by any constant (for example `2`)
would result in a solution where `y` was multiplied by the same constant.

That is (using `2` as our constant
`color(white)("XXX")x=2*2`
would imply that
`color(white)("XXX")y=1*2 =2`

But evaluating `x+2y=4`
with `x=2` does not give `y=2`

Therefore the equation is not a direct variation