This is also borderline not-an-answer, but it might be a nice broadening of your students' worldview to know that the "$m$" and the "$b$" are not universally accepted. Showing them this map (even though I do not know its original source, so it may not be accurate in its details) could help their thinking out a bit:
Substantial edit: I now no longer believe that the above map has very many if any of its details correct, although the general sentiment ("$mx + b$ is not a worldwide convention") is still correct. I went through all the languages of Wikipedia that had an article for Linear_equation and found the first mention of "[variable]x + [variable]" in the article. I kept the same absurd color-coding as the map, even though most of my results disagree with the map, even in Europe where languages map more precisely to countries.
First "$mx+b$-type expression" in each language's Wikipedia page for Linear_equation
So anyway, one way or another, even though the map is probably-wrong, there definitely isn't much worldwide agreement on which variables to use in which slot.