Question

How do you tell if an equation like `x+7y=0` or `2x+3y=1` is a direct variation?

Answer 1

If an equation can be manipulated into the form
`y = m*x` for some constant `m` then it is a direct variation (otherwise it is not).

To use your examples:
`x+7y=0`
`rarr 7y= -x`
`rarr y = (-1/7)x`
So this is a direct variation (with `m=(-1/7)`)

`2x+3y = 1`
`rarr 3y = -2x +1`
`rarr y = (-2/3)x +1/3`
Because of the additional term `+1/3` this can not be expressed as `y` equal to a constant multiplied by x.
So this is not a direct variation.