why is the slope of the line denoted as ‘m’?

I can give you the short answer: Because it is.

Everything else is just gravy.

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.”

From the second reference:

“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.”

In conclusion, I think the origin of this usage has been lost to the veil of time.