The "M" in the Formula for Slope
 

Nobody seems to know for sure why the letter “m” is to represent slope in the equation. Some mathematics professors have traced the use of it in equations to as far back as books from 1820. They comment that Descartes didn’t use the letter “m” in any of his work, though Euler did. In other words, nobody knows for sure, but these are some possibilities.

Possible explanations:

-         The choice may have been arbitrary; perhaps the first person to use the letter “m” in working the formula for slope simply picked the letter at random.

-         John Conway says: Perhaps it stands for “modulus of slope.” The term “modulus” has been known to be used for “the essential parameter of determining.”

-         It could stand for the French verb monter, which means “to go up,” “to ascend,” “to climb,” “to rise up,” “to slope up,” etc.

-         Similar possibilities from the French are “montaire”  for “mount” and  “montaigne” for “hill.”

-         Mons, which is the Latin noun for “mountain.”

-         M. Risi (author of books on mathematics) was once asked the question, and his reply: “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.”

-         One student says: “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 equation.”