# Why are slope and y-intercept m and b? **URL:** \ **Category:** Factual Questions\ **Created:** [November 23, 2010, 2:30am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613 "2010-11-23T02:30:43Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Strinka](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/strinka/32/512_2.png) [@Strinka](https://boards.straightdope.com/u/Strinka)\ **Post date:** [November 23, 2010, 2:30am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/1 "2010-11-23T02:30:43Z")
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? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 23, 2010, 2:34am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/2 "2010-11-23T02:34:02Z")
According to [this site](http://mathforum.org/library/drmath/view/65307.html), 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](http://jeff560.tripod.com/geometry.html) referenced within the aforementioned one, with no clear motivation given for the choice. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [November 23, 2010, 2:34am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/3 "2010-11-23T02:34:24Z")
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. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [November 23, 2010, 2:35am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/4 "2010-11-23T02:35:57Z")
We may not ever know for sure. [Here is one discussion](http://mathforum.org/library/drmath/view/52477.html) ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 23, 2010, 2:40am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/5 "2010-11-23T02:40:26Z")
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. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [November 23, 2010, 2:41am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/6 "2010-11-23T02:41:34Z")
> [@CookingWithGas](#): > > We may not ever know for sure. > > [Here is one discussion](http://mathforum.org/library/drmath/view/52477.html) From that page, I like this explanation: > [@](#): > > In our system, the first letters of > the alphabet, a, b , c… represent the constants, the last > letters, x, y, z represent the unknown variables and the middle > letters, m, n, p… represents the parameters. 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. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 23, 2010, 2:44am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/7 "2010-11-23T02:44:35Z")
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](http://jeff560.tripod.com/geometry.html) (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. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 23, 2010, 2:50am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/8 "2010-11-23T02:50:23Z")
(Much more constant but of course still not universally so, I should say) ---
**Author:** ![Dervorin](https://avatars.discourse-cdn.com/v4/letter/d/eb8c5e/32.png) [@Dervorin](https://boards.straightdope.com/u/Dervorin)\ **Post date:** [November 23, 2010, 10:54am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/9 "2010-11-23T10:54:02Z")
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: [Equation of a Straight Line](http://www.mathsisfun.com/equation_of_line.html) (scroll down to the footnote) > [@](#): > > Different Countries teach different “notation” (as sent to me by kind readers): > In the US, Canada and UAE the notation is: > y = mx + b > > In the UK, Australia, Bahamas, Brunei, Germany, Ghana, India, Indonesia, Ireland, Jamaica, Malaysia, Malta, Nepal, New Zealand, Pakistan, Singapore, Solomon Islands, South Africa, Zambia and Zimbabwe > y = mx + c > > In Brazil, Czech Republic, Denmark, Holland and Viet Nam: > y = ax + b > > In China, Finland, Russia and Ukraine: > y = kx + b > > In Greece: ψ = αχ + β > In Italy: y = mx + q > In Japan: y = mx + d > In Latvia: y = jx + t > In Romania: y = gA + C > In Sweden: y = kx + m > In Slovenia: y = kx + n 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. ---
**Author:** ![Norse](https://avatars.discourse-cdn.com/v4/letter/n/a9adbd/32.png) [@Norse](https://boards.straightdope.com/u/Norse)\ **Post date:** [November 23, 2010, 11:22am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/10 "2010-11-23T11:22:54Z")
> [@friedo](#): > > > [@](#): > > > > In our system, the first letters of > > the alphabet, a, b , c… represent the constants, the last > > letters, x, y, z represent the unknown variables and the middle > > letters, m, n, p… represents the parameters. 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 🆒 ---
**Author:** ![Balthisar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/balthisar/32/2825_2.png) [@Balthisar](https://boards.straightdope.com/u/Balthisar)\ **Post date:** [November 23, 2010, 1:07pm UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/11 "2010-11-23T13:07:08Z")
> [@Norse](#): > > 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) 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.) ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [November 23, 2010, 1:45pm UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/12 "2010-11-23T13:45:03Z")
Sorry, can’t read. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [November 23, 2010, 1:52pm UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/13 "2010-11-23T13:52:04Z")
> [@Balthisar](#): > > 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 ---
**Author:** ![Norse](https://avatars.discourse-cdn.com/v4/letter/n/a9adbd/32.png) [@Norse](https://boards.straightdope.com/u/Norse)\ **Post date:** [November 23, 2010, 2:09pm UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/14 "2010-11-23T14:09:32Z")
> [@Balthisar](#): > > Where were “counting variables” used in mathematics before the wide introduction of computers with interpreted/compiled languages? In sums of series, a concept which predates computers by quite a few centuries. [Wikipedia entry](http://en.wikipedia.org/wiki/Series_(mathematics)). ---
**Author:** ![Nancarrow](https://avatars.discourse-cdn.com/v4/letter/n/c37758/32.png) [@Nancarrow](https://boards.straightdope.com/u/Nancarrow)\ **Post date:** [November 23, 2010, 9:42pm UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/15 "2010-11-23T21:42:15Z")
In Soviet Russia, mx+b=_you_. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 23, 2010, 10:47pm UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/16 "2010-11-23T22:47:24Z")
> [@Dervorin](#): > > 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. 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? > [@Nancarrow](#): > > In Soviet Russia, mx+b=_you_. Okay, this made me laugh. ---
**Author:** ![Dervorin](https://avatars.discourse-cdn.com/v4/letter/d/eb8c5e/32.png) [@Dervorin](https://boards.straightdope.com/u/Dervorin)\ **Post date:** [November 23, 2010, 10:57pm UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/17 "2010-11-23T22:57:12Z")
> [@Thudlow\_Boink](#): > > 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? > > Okay, this made me laugh. I didn’t put quotes around my phrases; your numbers are much the same as I get when I do: 43,000 vs 24,600. My rapid search seems to have led me astray! ---
**Author:** ![GameHat](https://avatars.discourse-cdn.com/v4/letter/g/ed655f/32.png) [@GameHat](https://boards.straightdope.com/u/GameHat)\ **Post date:** [November 24, 2010, 3:37am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/18 "2010-11-24T03:37:34Z")
I don’t know about _b_, but back when I took Calculus I remember the teacher telling us _m_ came from _monter_, which is French for “to climb”. Made enough sense to me, but I don’t know if that’s the proper source. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 24, 2010, 4:22am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/19 "2010-11-24T04:22:18Z")
The explanation that it comes from the French word for “climb” is a mere folk history, unsupported by the evidence. ---
**Author:** ![Raiko](https://avatars.discourse-cdn.com/v4/letter/r/3da27b/32.png) [@Raiko](https://boards.straightdope.com/u/Raiko)\ **Post date:** [November 24, 2010, 5:24am UTC](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613/20 "2010-11-24T05:24:48Z")
The true answer is “because variables hate you.” [Next page](https://boards.straightdope.com/t/why-are-slope-and-y-intercept-m-and-b/561613.md?page=2)