Is there a specific format for writing "where variable x represents/is"

Question

For instance, I have the equation y = mx, where m is the slope. Is there a concise and mathematical way to write "where m is the slope"?

Answer 1

Not in that particular case (although I'm ready to be contradicted by somebody with a greater knowledge of mathematical notation), or at least not one which is better than writing "where m is the slope" in terms of conciseness and clarity. Sometimes, if one is defining a variable, they will use ":=" to indicate that this equality is by definition and not just some coincidence. Formal mathematics is a lot wordier than you might imagine, and the best way to define or to explain is often with words rather than clunky notation.