Subject: slope


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?


Hi Susan

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:

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.


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