Why b for Intercept?Date: 10/16/2003 at 12:07:04 From: Brian Subject: In y = mx + b, why b? In the slope-intercept formula y = mx + b Why is the letter "b" used to represent the y-intercept? It may be helpful to know that in class we established the reason for "m" representing the slope of the line. A famous French mathematician, Rene Decartes, invented the x-y plane. The French word meaning "to climb" is "monte". slope = climb = monte = m My guess is that whatever the "b" stands for, it has something to do with the French language. I know this is an obscure question, but any help you can offer would be greatly appreciated. Brian C. Date: 10/16/2003 at 13:08:28 From: Doctor Peterson Subject: Re: In y = mx + b, why b? Hi, Brian. As we have said elsewhere in our site, we don't believe that the m really comes from a French word: Math terms http://mathforum.org/dr.math/faq/faq.terms.html Why m for slope? http://mathforum.org/library/drmath/view/52477.html As far as we can tell, the form mx+b originated in some American textbook, and made enough sense to be copied by others. The letters used don't really matter; in other countries other forms such as ax+b and mx+c are common. Note that although Descartes did use x and y, he never used m! My impression is that most likely these letters were chosen in much the same as x and y, which don't stand for words: We use letters near the end of the alphabet for the unknown variables, x and y. We use letters near the beginning of the alphabet for the intercepts, a and b; these are in the same order as the axes they relate to, x and y. We use a letter in the middle of the alphabet, m, for the slope, to keep it distinct. Note that the intercepts appear prominently in the two-intercept form, which many students never see: x y --- + --- = 1 a b Using a and b makes this form very neat and memorable. And I think that is all that is behind this choice of letters. Of course, that is just my impression; I never got to interview the first author to use this form and ask why he did it! If you have some historical evidence to support an alternative theory, I'd like to hear it. According to Jeff Miller's page http://jeff560.tripod.com/geometry.html it appears that m was used before a and b, perhaps originating with mx+n; that may have become established first rather than after a and b as my summary implies, but the order doesn't matter. Note that he says O'Brien used m for slope again in 1844 in _A Treatise on Plane Co-Ordinate Geometry_ [V. Frederick Rickey]. George Salmon (1819-1904), an Irish mathematician, used y = mx + b in his _A Treatise on Conic Sections_, which was published in several editions beginning in 1848. Salmon referred in several places to O'Brien's _Conic Sections_ and it may be that he adopted O'Brien's notation. Salmon used a to denote the x-intercept, and gave the equation (x/a) + (y/b) = 1 [David Wilkins]. This lends support to my proposal. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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