Question

Is `y=2x+1` a direct variation and if it is, how do you find the constant?

Answer 1

It is a direct variation and the constant of variation is the slope of the line, which is 2.

Answer 2

Alternative view
`y= 2x +1` is not a direct variation.

To be a direct variation multiplying one of `x` or `y` by some constant `k` should cause the other to be multiplied by the same amount.

For example `(x,y) =(1, 3)` is one solution pair for this equation.

If we let `k=5`
then
`color(white)("XXXX")` `(5(1), 5(3)) = (5, 15)` should also be a solution pair.

but `x=5`
`rArr y = 11`

So this is not a direct variation.

Note: `y=2x` would be a direct variation.