Wednesday, 20 February 2013

Why M for Slope

A new post of this is available at

Over the many years I taught I developed a keen interest in the origin and use of the symbols and terminology of math. When the internet came around I jumped in pretty early with a web page on Mathwords, contributing on the Dr Math and Teacher to Teacher support Math Forum, and for several years, this blog. Over that time there are few questions that come up more often than the reason for the letter m as the symbol for slope in the standard American (and it does seem to be mostly American) linear slope intercept equation form, y = mx + b.
Almost no one seems to ask about the b, which is even more curious to me.


Anonymous said...

In German textbooks the standard linear equation is:

y = mx + t

Belfry Bat said...

What may be ironic, I can't find any evidence for "slupan-" ever having been a Latin stem; OED pleads obscurity over the origin of "slope" older than "aslope" of 15C; it certainly does not look like a Latin word, with that "sl", but rather germanic or perhaps gaelic, like "slogan" and perhaps "slough". The most-Continental "sl-" in English I can think of would be "slovene", which seems to come from Slavonic "slovene".

Good Latin words for slope-like things seem to include the stem "clin-" remembered in the English "incline". The French "pent-" words are wholy mysterious to me. Latin "pend-" is about hanging and weighing; the "paen-" and "poen-" are related to English "pain" and "punnish", and perhaps "repent", but the similar Latin participle "repente" is about crawling or creeping, hence "reptile".

One might wildly conjecture that some misguided scholar-brittons post-Guillaume were talking with eachother about some "escline", eventually sluring it into something like "slip", as the Gauls and Franks gradually beat the grecco-latin "schola" into "escole" and eventually "école" which found its way into German as "Schüle", but there seems no textual record of such an evolution.

Luke Robinson said...

Here in the UK we use y=mx+c.

Rob said...

It may not be historically relevant, but since we use it, the reason I give my students is this: "B is for where we Begin, M is for how we Move." It makes some intuitive sense, which in turn assists in them remembering which is which.

Gregory Taylor said...

I found this website compiled from reader remarks:
...When I was posting up a rant about variables on my blog. My issue is mostly with the 'h' and 'k' in vertex form of the parabola, because while 'm' is pretty consistently slope in North America, 'k' is all over the map. (

I also suspect no one really asks about the 'b' because 'a' is often used for the x-intercept, so it sort of follows naturally. (Though 'a' has it's own issues.) Anyway, thanks for the history!

Pat's Blog said...

Belfry Bat, I think the Latin was something more like lubricious, from which we get slippery (think "lubricated"). The Latin seems to come from the Proto indo Euro root slupan or sleubh- Here is from webpage "",
derived from the English word lubricous
derived from the Latin word lubricus (slippery; sinuous; inconstant)
derived from the Proto-Indo-European root *sleubh-

Perhaps my assertion to Latin was a little too direct. Thanks for the note.

Unknown said...

Paul Foerster said...

I can confirm Hector Hirigoyen's statement about the origin of "m" for slope. Hector was in the audience when I did a presentation at a math teachers' meeting in Florida about 1986 or 1987. His point was that "m" came from the French "montant," meaning "the rise." Because he taught AP French as well as mathematics, it seemed like a logical conclusion.

I was so thrilled with this new knowledge that I told it to my BC Calculus class when i returned to San Antonio. To add to the credibility, I asked Cassandra Stapfer, my exchange student from Paris, to confirm that this was correct. Cassandra said, "montant does mean 'the rise,' but in France we use 's' for 'slope'."So much for my brilliant discovery!

I did figure out why it was logical to use "b" for the y-intercept. It seemed obvious that "a" was used for the x-intercept, as in the intercept form of the linear function equation, (x/a) + (y/b) = 1. Thanks for confirming my thought in this regard!