Why is $m$ used to denote slope? What is the reason, historically, that the letter $m$ is used to denote the slope of a line?
 A: According to Wolfram MathWorld, there's no consensus. Some think it may have come from French monter meaning to climb, but this is just speculation $-$ it's likely just a trend that caught on. The article I linked to contains a greater elaboration and some examples of where it's not used.
A: 
It is not known why the letter m was chosen for slope; the choice may have been arbitrary. John Conway has suggested m could stand 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. However, there is no evidence to make any such connection. Descartes, who was French, did not use m. In Mathematical Circles Revisited (1971) mathematics historian Howard W. Eves suggests "it just happened."

Source
A: Not a reason, but a lovely coincidence is that the higher dimensional analogue of a slope is a matrix.
$$
\vec{y} = M(\vec{x})
$$
would be the higher dimensional analogue of 
$$
y = mx
$$
where $\vec{y} \in \mathbb{R}^m$, $\vec{x} \in \mathbb{R}^n$, and $M$ is a $n \times m$ matrix.
So I like to think of the "m" as standing for "matrix".
