Slope is the rise and fall of an incline. While there is no absolute, known reason why Americans use the letter “M” to represent slope in a linear equation, there are a few theories and speculations.
Did We Get it From the French?
One guess as to why “M” is used for slope has to do with the French word for climb, “monter;” another explanation is because both mountains and movement begin with the letter “M.” If “M” is derived from the French word for climbing, that would be ironic, because the French do not use “M” to denote slope in an equation; rather they use “A” for slope, perhaps because of "ascending" or "Alps," though that is not known for certain either. Slope is also sometimes called “modulus of slope,” which begins with the letter “M.”
Sloping Around the World
Many countries, such as Sweden, Norway, Russia and Austria use the letter “K” for slope, probably to stand for “koefficient,” their native spelling of English’s “coefficient.” This makes sense because slope is the ratio for the rise between two points; however, it has no correlation for why Americans use “M.”
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