Question

Is `y-x=4` a direct variation equation?

Answer 1

No.
A direct variation equation has the form or can be converted into the form:
`y = mx` for some constant value `m`

One observation that follows from this is that if `x=0` then `y=0`;
this condition is clearly not true for the given equation.

A second observation is that for a direct variation equation doubling the value of `x` (or multiplying it by any value) causes the value of `y` to be multiplied by that same value;
again this is not true for the given equation.

Answer 2

No. A direct variation equation defines a line that goes through the origin, `(0,0)`.

`y-x=4` does not satisfy that requirement.

The equation in slope-intercept form is `y=x+4`. If `x=0`, then `y=4`. So this equation is not a direct variation.