The Origin of "m" in Linear Functions

[Quadratic]

The origin of "m"?

Why is it that linear functions are often expressed in terms of f(x)="m"x+b? I mean, when dealing with all the other polynomials, we follow the typical f(x) = ax^n + bx^(n-1) + cx^(n-2)... so where did "m" come from? Why don't all textbooks just express it as f(x) = ax+b?

 

[jcsd]

J. Miller has undertaken a detailed study of the origin of the symbol m to denote slope. The consensus seems to be that it is not known why the letter m was chosen. 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." However, there is no evidence to make any such connection. In fact, Descartes, who was French, did not use m (Miller). Eves (1971) suggests "it just happened."

http://mathworld.wolfram.com/Slope.html

 

[tacman]

The use of "m" in linear functions dates back to the early 17th century when French mathematician René Descartes first introduced the Cartesian coordinate system. In this system, the x-axis represents the independent variable and the y-axis represents the dependent variable. To represent a linear relationship between these two variables, Descartes used the equation y=mx+b, where "m" represents the slope of the line and "b" represents the y-intercept. This notation has since become a standard way of expressing linear functions.

The use of "m" in place of "a" in the general polynomial equation (f(x) = ax^n + bx^(n-1) + cx^(n-2)...) is due to the fact that in linear functions, the slope "m" is a constant value, while the other coefficients (a, b, c, etc.) may vary depending on the degree of the polynomial. This makes it easier to differentiate between the two types of functions.

Furthermore, the letter "m" is commonly used in mathematics to represent slope, as it comes from the French word "montée" which means "rise" or "climb". This further reinforces its use in linear functions, where the slope represents the rate of change or "climb" of the line.

In short, the use of "m" in linear functions is a historical convention that has become widely accepted and is now a standard way of representing these types of functions. While it may seem unusual compared to the notation used for other polynomials, it serves a specific purpose and has a logical origin in the Cartesian coordinate system.