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Why m for slope?

Date: Wed, 9 Nov 1994 15:44:42 -0800 (PST)
From: Mary Koch

Dr. Math:

My class wants me to ask you why the letter m was selected to 
represent slope.


Date: Sat, 12 Nov 1994 07:28:39 -0500
From: Stephen Weimar
Subject: Re: why "m" for slope

>Date: Fri, 11 Nov 94 23:47:50 EST
>Subject: Re: why "m" for slope
>Why call slope m has been a question that has been researched by 
>math historians but has not been answered definitively yet.  All the 
>usual suggested "reasons" have proven false.  One math historian has 
>been doing a search for a few years for the earliest use in a math book.
>So the jury is still out on this question.
>Erica Voolich

From: "John Conway"
Date: Sun, 13 Nov 94 19:38:58 EST
Subject: Re: why "m" for slope?

I believe (but am not sure) that what we now call just the
"slope" was once called the "modulus of slope", the word
"modulus" being used in its sense of "number used to
measure" (as in "Young's modulus").

    Descartes' "La Geometrie" doesn't use the "m" in this
connection, but I seem to remember that Euler often does.

Descartes makes no use of Greek letters for parameters in
his Geometrie, and most later authors have followed him in
this, if we except the use of theta, phi  for variable

    This is an interesting question - I'll try to track it back.

               John Conway

Date: Mon, 19 Feb 1996 08:52:40 -0500 (EST)
From: John Conway

    When this question came up last year, it emerged that many
people have been taught that it comes from the French, "monter",
to climb.  I think this is an "urban legend".

    I don't have much faith in the theory I put forward then -
that this  m  stands for "modulus of slope".  It is true that
the term "modulus" has often been used for "the essential parameter

    John Conway

Date: Mon, 19 Feb 1996 10:07:33 -0500
From: André Deschênes
Organization: Le Petit Séminaire de Québec

I recently met a former Mathematics book writer, M. Risi, who wrote 
some books for teaching mathematics at a level that is about the 
same as pre-college.  These books where written in French for 
students of Quebec province.  I asked him exactly the same question 
as yours:  "Why did you use m for slope?  No French word 
beginning with the letter m seems to me appropriate to represent slope, 
and I don't know an English word either." 

His answer was approximately:  "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.  When we started the 
explanations of slope, it was in studying the first degree 
equation:  y = mx + b.  x and y were the variables, b was fixed and 
considered as a constant, and what was appended to the 
coefficient of x as its value varied.  So it was a parameter and 
that is why we used m."

André Deschênes

Date: Mon, 19 Feb 1996 12:38:34 -0500 (EST)
From: John Conway

     But M. Risi  plainly wasn't the first person to use "m" in this

     It interests me that on this continent the typical form is
y = mx + b,  whereas in England and in "the" Continent  it is
y = mx + c.   The latter form still seems to me to be more natural,
since this "c" is like the arbitrary constants in indefinite
integrals,  and so it will probably be very hard to date.  But
the "b" usage probably originated with the author of a particular
influential North American textbook, and maybe we can find out
just who it was.

    John Conway

From: "G. A. Edgar" <>
Newsgroups: sci.math
Subject: Re: Why "m" for slope?
Date: Thu, 09 Sep 1999 06:50:26 -0400
Organization: The Ohio State University

Where did this question come from?  It is asked like clockwork
every September.  Let me just quote an answer from 1996:

> Subject: Re: QUESTION: M = slope? IN GEOMETRY
> Email:
> Date: 1996/12/21
> Forums:       k12.ed.math 
> According to one of the most eminent mathematics historians in
> the US who has researched the topic, Professor Frederick
> Rickey, Bowling Green University, Ohio, we do NOT know why m
> was used for slope in the slope/intercept form of the
> equation.  Book authors who give the French connection are
> WRONG.  Professor Rickey says there is absolutely no proof for
> the the French connection.
> Now, if someone knows another math historian with a better
> reputation than Dr. Rickey who disputes Rickey's claim, please
> let me know.
> ---
> Karen Dee Michalowicz                  Adjunct Faculty
> Upper School Mathematics Chair         George Mason University        
> The Langley School                     Fairfax, VA
> McLean, VA
> Treasurer,
> HPM (History/Pedagogy of Mathematics), Americas Section

> Subject:      Re: y=mx+b
> Author:       V. Frederick Rickey <>
> Date:         Sat, 24 May 1997 14:56:52 -0400
> Yes, in 1990 I did write a brief note in the HPM Newsletter about the
> origin of the word slope. Since then I have pushed the first use of the
> word (that I know of) back to 1850. Before that phrases such as "the
> tangent of the angle between the line and the x-axis" were used. I take
> this as evidence that the concept of slope had not crystalized and so name
> was attached to it. Both the word "slope" and the use of the letter "m"
> seem to have originated in the USA.
> Unfortunately, I am not now in a position to post a detailed reply as I am
> on my way out of town. I will do so in July.
> Fred Rickey

Gerald A. Edgar 
Department of Mathematics
The Ohio State University
Columbus, OH 43210

Date: Tue, 3 Oct 2000 22:23:20 -0400 (EDT)
From: Robby
Subject: Re: why "m" for slope

I came across the question in your FAQ and I just wanted to say that I 
think of m as standing for "move" and b  for "begin." This relates to the 
way you graph linear equations by hand. You can use the b value to plot 
the "beginning" point (0,b). Then the m value instructs you where to "move" 
from point (0,b) to plot the next point, thus giving you the line for the 

Just another idea (and a simple way to teach linear equations!)

Robby "Math-freak" Grant
Associated Topics:
High School History/Biography

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