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  #1  
Old 11-22-2010, 08:30 PM
Strinka Strinka is offline
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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  
Old 11-22-2010, 08:34 PM
Indistinguishable Indistinguishable is online now
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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 08:37 PM..
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  #3  
Old 11-22-2010, 08:34 PM
friedo friedo is offline
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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.
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  #4  
Old 11-22-2010, 08:35 PM
CookingWithGas CookingWithGas is offline
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We may not ever know for sure.

Here is one discussion
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  #5  
Old 11-22-2010, 08:40 PM
Indistinguishable Indistinguishable is online now
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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 08:43 PM..
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  #6  
Old 11-22-2010, 08:41 PM
friedo friedo is offline
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Quote:
Originally Posted by CookingWithGas View Post
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.
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  #7  
Old 11-22-2010, 08:44 PM
Indistinguishable Indistinguishable is online now
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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 08:49 PM..
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  #8  
Old 11-22-2010, 08:50 PM
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(Much more constant but of course still not universally so, I should say)

Last edited by Indistinguishable; 11-22-2010 at 08:50 PM..
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  #9  
Old 11-23-2010, 04:54 AM
Dervorin Dervorin is offline
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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.
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  #10  
Old 11-23-2010, 05:22 AM
2square4u 2square4u is offline
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Quote:
Originally Posted by friedo View Post
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
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  #11  
Old 11-23-2010, 07:07 AM
Balthisar Balthisar is online now
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Quote:
Originally Posted by 2square4u View Post
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.)
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  #12  
Old 11-23-2010, 07:45 AM
Derleth Derleth is online now
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Sorry, can't read.

Last edited by Derleth; 11-23-2010 at 07:45 AM..
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  #13  
Old 11-23-2010, 07:52 AM
naita naita is offline
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Quote:
Originally Posted by Balthisar View Post
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 07:53 AM.. Reason: ETA: ETA
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  #14  
Old 11-23-2010, 08:09 AM
2square4u 2square4u is offline
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Quote:
Originally Posted by Balthisar View Post
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.
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  #15  
Old 11-23-2010, 03:42 PM
Nancarrow Nancarrow is offline
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In Soviet Russia, mx+b=you.
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  #16  
Old 11-23-2010, 04:47 PM
Thudlow Boink Thudlow Boink is offline
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Quote:
Originally Posted by Dervorin View Post
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 View Post
In Soviet Russia, mx+b=you.
Okay, this made me laugh.
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  #17  
Old 11-23-2010, 04:57 PM
Dervorin Dervorin is offline
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Quote:
Originally Posted by Thudlow Boink View Post
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!
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  #18  
Old 11-23-2010, 09:37 PM
GameHat GameHat is offline
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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.
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  #19  
Old 11-23-2010, 10:22 PM
Indistinguishable Indistinguishable is online now
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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 10:22 PM..
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  #20  
Old 11-23-2010, 11:24 PM
Raiko Raiko is offline
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The true answer is "because variables hate you."
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  #21  
Old 11-24-2010, 12:28 AM
Cunctator Cunctator is offline
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Quote:
Originally Posted by Dervorin View Post
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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