algebra I (6-9)
I am a secondary school teacher. My students and I would like to know why the
letters m and b are traditionally used to stand for slope and Y-intercept in the
standard form of an equation. Was this an arbitrary choice? Who made it? Are the
letters from Greek ot Latin words?
We received the same question from Julie a while ago and I
had to reply that I didn't know. That is still my answer but now at least I can
give a reference to the fact that some other people who have wondered about
this question don't know the answer either. There is a list compiled by Jeff
Miller called the "Earliest Uses of Various Mathematical Symbols". The URL is
In this list under "m" is the entry:
m FOR SLOPE.
I do not have the first use of m for slope. In a message to the math history
mailing list in January, Dave Cohen of UCLA offered a use in the 1855 edition of
Todhunter's Treatise on Plane Co-Ordinate Geometry (Cambridge: Macmillan & Co.,
1855). Todhunter uses m to denote the tangent of the angle of inclination of a
line and he writes the slope-intercept equation of the line as y = mx + c.
A message posted in sci.math stated that V. Frederick Rickey had found a use of m
in the 1820s. (I have asked Dr. Rickey for more information.)
It is not known why the letter m was chosen for slope; the choice may have been
arbitrary. John Conway has suggested m stands for "modulus of slope." One high
school algebra textbook says the reason for m is unknown, but remarks that it is
interesting that the French word for "to climb" is monter. Several experts
believe there is no connection here; Descartes, who was French, did not use m.