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

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The equation y=mx+b uses 'm' for slope and 'b' for y-intercept, with 'm' likely derived from the French word "mont," meaning mountain, reflecting the concept of slope. The 'b' may originate from polynomial notation, where it appears as a constant term in equations like y=ax^n+bx^(n-1). Different countries use varying symbols for these components; for instance, Italy uses 'q' instead of 'b', and Norway refers to 'm' as 'a'. The discussion highlights the variations in mathematical notation across cultures. Understanding these origins can clarify the equation's components and their significance in linear functions.
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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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