Using Google, I see a lot of variation around the world.

y = mx + b

y = ax + b

y = mx + c

y = kx + b

y = mx + n

y = px + q

Some European countries (and possibly others) don't say 'slope'. They say 'direction coefficient'. My favorite idea is the following.

When we pick letters of the alphabet to represent numbers, we generally pick beginning letters for constants {a,b,c,d,e} and ending letters for variables {u,v,x,y,z} and letters in the middle for parameters (k,m,n}. Slope is a parameter. So somebody picked m, and it caught on (in the US, anyway).

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