What is the reason, historically, that the letter $m$ is used to denote the slope of a line?
Why is $m$ used to denote slope?
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analytic-geometry
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1In elementary school (later years) in Sweden, $m$ usually denotes the intercept, as you can see here: http://sv.wikipedia.org/wiki/Linjär_ekvation – 2012-01-31
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2‘We designate the slope of a line by m because the word slope starts with the letter m; I know of no better reason.' – 2012-01-31
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0I believe it comes from the phrase modulus of slope. – 2017-01-21
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1For purposes of cross-reference, [this question is also asked on math ed SE](https://matheducators.stackexchange.com/questions/12796/explaining-to-students-why-m-and-b-are-used-in-the-slope-intercept-equation). There are a number of very good answers there. – 2018-01-07
2 Answers
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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.
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0See Also: http://jeff560.tripod.com/geometry.html. There is a huge section on slope, and seems to agree that the reason $m$ was chosen is not clear. – 2012-01-31
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0Thank you Clive. I saw the MathWorld page, I was hoping someone knew more than what was written there. – 2012-01-31
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0@Jim: I think that, short of undertaking some hardcore historical analysis, we'll have to make do with the answer that no-one knows the answer. – 2012-02-01
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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".