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

Dec 15, 2017

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

#### Explanation:

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

$y = k x$

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

Since $y = 2 x + 1$ 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.