Origin of y=mx+b: Explaining Slope & Y-Intercept

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Discussion Overview

The discussion centers around the notation used in the linear equation y=mx+b, specifically the choice of 'm' for slope and 'b' for y-intercept. Participants explore the origins and variations of these symbols across different languages and contexts.

Discussion Character

  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant suggests that 'm' derives from "mont" or "mount," relating to the concept of slope, while the origin of 'b' is uncertain but speculated to relate to terms like base or low point.
  • Another participant proposes that 'b' may come from the convention of writing polynomials, where 'b' appears in the general form of polynomial equations.
  • Several participants note that different countries use different symbols for these concepts, such as 'q' in Italy for y-intercept, 'a' in Norway for slope, and 'c' in Britain for y-intercept.
  • A later reply humorously comments on the perceived strangeness of these variations in notation.

Areas of Agreement / Disagreement

Participants express various hypotheses regarding the origins of the symbols, but there is no consensus on the definitive reasons for the choices of 'm' and 'b'. The discussion remains open with multiple competing views.

Contextual Notes

Limitations include the lack of definitive sources for the origins of the symbols and the dependence on cultural and linguistic variations in mathematical notation.

Liger20
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Hello, could someone please explain to me why the equation y=mx+b uses 'm' for slope and 'b' for y-intercept? This has always bothered me for some reason.
 
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"m" comes from "mont", or "mount", or some french or latinized word meaning mountain, or sloping grade. The "b", I'm not sure about. Maybe (just a wild guess) base, bass, some word meaning low point, like where the "mountain" meets the "flat". I'm more certain about the "m" for "mont" as the slope.
 
Liger20 said:
Hello, could someone please explain to me why the equation y=mx+b uses 'm' for slope and 'b' for y-intercept? This has always bothered me for some reason.

The b problably comes from the fact that polynomials are typically written y=ax^n+bx^n-1+cx^n-2 etc. But the special case of a linear polynomial a=m (from what symboipoint said) and the b probably just stayed.
 
In Italy, they don't use b, they use q.
 
In norway, m is called a.
 
And in Britain, 'b' is called 'c'!
 
Wow, you guys have really strange alphabets!
 
I always enjoyed n \cdot p_0 = n \cdot \left[ \begin{array}{c}x\\y\end{array} \right]
 

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