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History of the y-intercept

Date: 03/18/2002 at 08:11:37
From: Chris Yang
Subject: The history of the y-intercept

Why does the variable 'b' represent the y-intercept?

I've tried researching it but I can't find the answer.

Thank you for your time,
Chris Yang

Date: 03/18/2002 at 12:34:43
From: Doctor Peterson
Subject: Re: The history of the y-intercept

Hi, Chris.

It is common to write the slope-intercept form as y = mx + b, but that 
is no more than custom, and perhaps only in America. I suspect that 
this tradition arose from teaching several different forms of the 
equation of a line together, so that the same parameter names were 
used in each. Since one form uses BOTH the x- and y-intercepts, namely

    x/a + y/b = 1

it was natural to use consecutive letters a and b for the x- and 
y-intercepts. The "a" disappears in other forms, but the "b" remains.

For more about the historical use of the different variables used for 
Slope, see Jeff Miller's Earliest Uses of Symbols from Geometry:   

- Doctors Peterson and Sarah, The Math Forum   
Associated Topics:
High School Equations, Graphs, Translations
High School History/Biography

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