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Why is 'b' Used in Slope-Intercept Form?

Date: 02/04/2004 at 19:43:02
From: Lucas
Subject: Why is the letter "b" used for the y intercept in equations?

My class has to find out the origin of the letter "b" used for the 
y-intercept in equations.  For example, did it come from a word in 
another language having something to do with the y-intercept? 



Date: 02/04/2004 at 21:35:11
From: Doctor Rob
Subject: Re: Why is the letter "b" used for the y intercept in equations?

Thanks for writing to Ask Dr. Math, Lucas!

The likely reason for using b for the y-intercept comes from a
seldom seen form for the equation of a line.  It applies only to
lines neither vertical, nor horizontal, nor passing through the
origin.  It is called the two-intercept form:

   x/a + y/b = 1.

Then the x-intercept is a and the y-intercept is b.  Probably a
and b are used because they are the first two letters of the
alphabet.

Solving for y, you can convert this form to slope-intercept form,
and you get

   y = (-b/a)*x + b,

so the slope is m = -b/a, and the y-intercept is b.

Feel free to write again if I can help further.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Linear Equations

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