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#1
11-22-2010, 09:30 PM
 Strinka Member Join Date: Dec 2004 Location: My own little world Posts: 1,730
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?
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#2
11-22-2010, 09:34 PM
 Indistinguishable Guest Join Date: Apr 2007 Posts: 10,519
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.

Last edited by Indistinguishable; 11-22-2010 at 09:37 PM.
#3
11-22-2010, 09:34 PM
 friedo Guest Join Date: May 2000 Location: Brooklyn Posts: 23,421
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.
#4
11-22-2010, 09:35 PM
 CookingWithGas Charter Member Join Date: Mar 1999 Location: Tysons Corner, VA, USA Posts: 11,495
We may not ever know for sure.

Here is one discussion
#5
11-22-2010, 09:40 PM
 Indistinguishable Guest Join Date: Apr 2007 Posts: 10,519
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.

Last edited by Indistinguishable; 11-22-2010 at 09:43 PM.
#6
11-22-2010, 09:41 PM
 friedo Guest Join Date: May 2000 Location: Brooklyn Posts: 23,421
Quote:
 Originally Posted by CookingWithGas We may not ever know for sure. Here is one discussion
From that page, I like this explanation:

Quote:
 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.
#7
11-22-2010, 09:44 PM
 Indistinguishable Guest Join Date: Apr 2007 Posts: 10,519
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.

Last edited by Indistinguishable; 11-22-2010 at 09:49 PM.
#8
11-22-2010, 09:50 PM
 Indistinguishable Guest Join Date: Apr 2007 Posts: 10,519
(Much more constant but of course still not universally so, I should say)

Last edited by Indistinguishable; 11-22-2010 at 09:50 PM.
#9
11-23-2010, 05:54 AM
 Dervorin Guest Join Date: Jan 2006 Location: London Posts: 2,344
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)

Quote:
 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.
#10
11-23-2010, 06:22 AM
 2square4u Guest Join Date: Oct 2010 Location: 63°N, CET (GMT+1) Posts: 1,234
Quote:
Originally Posted by friedo
Quote:
 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
#11
11-23-2010, 08:07 AM
 Balthisar Charter Member Join Date: Nov 2000 Location: Southeast Michigan, USA Posts: 10,350
Quote:
 Originally Posted by 2square4u 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.)
#12
11-23-2010, 08:45 AM
 Derleth Guest Join Date: Apr 2000 Location: Missoula, Montana, USA Posts: 19,826

Last edited by Derleth; 11-23-2010 at 08:45 AM.
#13
11-23-2010, 08:52 AM
 naita Guest Join Date: Jun 2002 Location: Norway Posts: 4,898
Quote:
 Originally Posted by 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

Last edited by naita; 11-23-2010 at 08:53 AM. Reason: ETA: ETA
#14
11-23-2010, 09:09 AM
 2square4u Guest Join Date: Oct 2010 Location: 63°N, CET (GMT+1) Posts: 1,234
Quote:
 Originally Posted by 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.
#15
11-23-2010, 04:42 PM
 Nancarrow Guest Join Date: Oct 2004 Posts: 1,697
In Soviet Russia, mx+b=you.
#16
11-23-2010, 05:47 PM
 Thudlow Boink Charter Member Join Date: May 2000 Location: Lincoln, IL Posts: 24,090
Quote:
 Originally Posted by 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?

Quote:
 Originally Posted by Nancarrow In Soviet Russia, mx+b=you.
#17
11-23-2010, 05:57 PM
 Dervorin Guest Join Date: Jan 2006 Location: London Posts: 2,344
Quote:
 Originally Posted by 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!
#18
11-23-2010, 10:37 PM
 GameHat Guest Join Date: Dec 2007 Location: NW Chicago Suburbs Posts: 2,363
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.
#19
11-23-2010, 11:22 PM
 Indistinguishable Guest Join Date: Apr 2007 Posts: 10,519
The explanation that it comes from the French word for "climb" is a mere folk history, unsupported by the evidence.

Last edited by Indistinguishable; 11-23-2010 at 11:22 PM.
#20
11-24-2010, 12:24 AM
 Raiko Guest Join Date: Nov 2010 Posts: 59
The true answer is "because variables hate you."
#21
11-24-2010, 01:28 AM
 Cunctator Charter Member Join Date: Mar 2004 Location: Sydney, NSW, Australia Posts: 11,386
Quote:
 Originally Posted by Dervorin 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
It was y = mx + b at my school in Australia in the 1970s.

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