Notation to express affine relationship

Question

As you know, if we have a linear relationship between two variables $x$ and $y$ : $y=ax$, this is usually denoted by ,

$y\varpropto x $ y is proportional to x.

The question is if they are affinely related to each other, i.e. $y=ax +b$, what is the common notation to express that?

Answer 1

You're not going to get it with a single symbol. Two possibilities:

• $\exists a,b:y=ax+b$
• $\exists b:y-b\varpropto x$

If the context isn't clear you may need to specify that $a$ and/or $b$ are real; e.g., $\exists a,b\in\mathbb{R}:y=ax+b$.