8
$\begingroup$

What is the reason, historically, that the letter $m$ is used to denote the slope of a line?

  • 1
    In elementary school (later years) in Sweden, $m$ usually denotes the intercept, as you can see here: http://sv.wikipedia.org/wiki/Linjär_ekvation2012-01-31
  • 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
  • 0
    I believe it comes from the phrase modulus of slope.2017-01-21
  • 1
    For 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 2

7

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.

  • 0
    See 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
  • 0
    Thank you Clive. I saw the MathWorld page, I was hoping someone knew more than what was written there.2012-01-31
  • 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
0

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".