# Why are slope and y-intercept m and b?

In the equation y=mx+b. I’m not asking about what it means, I understand that.

But why m and b? Were all the other letters taken?

They’re certainly not initials, at least not in English. Maybe in Latin, if this convention is old enough?

According to this site, the b is probably from writing x/a + y/b = 1, the beginning of the alphabet being just as good as the end to impulsively draw letters from. The m, on the other hand, just seems to be some (even more idiosyncratic) quirk of history, dating to an earlier practice of writing y = mx + n. Why m and n (apart from their adjacency and similarity, which has them often being used for complementary data even today)? It’s unclear… the earliest known appearance is in an obscure 18th-century Italian text, according to this site referenced within the aforementioned one, with no clear motivation given for the choice.

The Y-intercept is b because the X-intercept is a, as in the highly-useful but rarely-taught double-intercept form, x/a + y/b = 1.

As for m, I don’t know, except that letters in the middle of the alphabet (i, j, m, n, etc.) are often used to indicate that they’re standing for something different than those in the beginning (a, b, c, etc.) and those at the end, which are usually your variables.

We may not ever know for sure.

Here is one discussion

There is also apparently a common academic folk history claiming that the m comes from the French noun for climb, “montée”, via Descartes. However, there is no evidence for this connection; in particular, Descartes does not actually use the letter m for slope.

From that page, I like this explanation:

Although I really don’t think “parameter” is the correct word; it’s just two distinct groups of constants so you use two distinct groups of letters for them.

But what’s the evidence for that theory? Is it even really true that people are or ever were often first exposed to lines with the point of view that the Y-intercept is to be taken as “constant” while the slope is to be taken as a “parameter” (with whatever connotations those imply)?

The interesting thing is that it seems, historically, from this site (linked above) that while the letter used for the Y-intercept has varied widely, the use of the letter m for the slope has been much more constant.

(Much more constant but of course still not universally so, I should say)

To add to the confusion: I was always taught the slope-intercept form as y = mx + c, and a quick round with Google appears to bear out my hypothesis that this is more common than y = mx + b. The former gets about 10 million hits, while the latter only gets about 1.5 million.

This appears to be a North America / Rest of World divide, at least according to this site: http://www.mathsisfun.com/equation_of_line.html (scroll down to the footnote)

So it looks entirely arbitrary; I don’t recall anyone explaining why these particular symbols were chosen, but I have happily perpetuated this in my own teaching.

Naah… Weeelll…

This is not universal. Where I come from, the first letters of the alphabet, a, b , c… usually represent real number constants (integers or non-integers), the last letters, x, y, z represent the unknown variables, the middle letters, i, j, k,… represent counting variables (integers) and n, m,… represent “arbitrarily large numbers” (usually integers)

and thus, y=ax+b is more logical, because a and b can very well be non-integers

Where were “counting variables” used in mathematics before the wide introduction of computers with interpreted/compiled languages? (Serious question; I’m not attacking your statement.)

I suspect capital sigma and pi notation predates computers.

ETA: Oh, and Norway uses y = ax + b which goes well with classics such as y = ax^2 + bx +c

In sums of series, a concept which predates computers by quite a few centuries. Wikipedia entry.

In Soviet Russia, mx+b=you.

And I’m getting different results (56,200 for “y = mx + b”; 29,100 for “y = mx + c”). Maybe because I’m putting quotation marks around them? or because I’m googling from a different location?