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I believe rozo711 has come closest to an accurate answer. I just have one or two pieces to add and the link below will help. I believe slope is represented by an 'm' due to the Latin word 'modus' which means measure. See the link below for more details.
It is said it is because the m stood for modulus.
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.
because m was once called modulus.
The slope is rise over run
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