Question

How do you tell wether the equation `y = 2x + 1` represents direct variation and if so, how do you identify the constant of variation?

Answer 1

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

Explanation:

2 variables which are directly proportional can be written in the form

`y=kx`

for some constant `k`. This means that if either `x` or `y` is doubled, the other is doubled as well.

Since `y=2x+1` does not pass through the origin (i.e. there exists the constant term of `1`), the variables `y` and `x` are not directly proportional - though, they do have a linear relationship.