document.write( "Question 341887: I have a question about the equation, \"y=mx+b\" Why is \"m\" the slope, and why is \"b\" the intercept? Please explain specifically.\r
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Algebra.Com's Answer #244805 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "The x-coordinate of the x-intercept is labeled \"a\" and the y-coordinate of the\r\n" );
document.write( "y-intercept was labeled \"b\". That was logical because \"a\" comes just before \"b\"\r\n" );
document.write( "in the alphabet, just as \"x\" comes just before \"y\".  In olden days they used\r\n" );
document.write( "the intercept form for the equation of a line instead of the slope-\r\n" );
document.write( "intercept form,.  The intercept form of a line is:\r\n" );
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document.write( "where a is the x-coordinate of the x-intercept and b is the y-coordinate of the\r\n" );
document.write( "y-intercept.  This is somewhat analogous to the equation for an ellipse\r\n" );
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document.write( "whose center is at the origin and whose x-intercepts are (帶,0) and whose y-intercepts are (0,帳).\r\n" );
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document.write( "The slope \"m\" of any slanted line can be defined in terms of the\r\n" );
document.write( "intercepts by the equation .\r\n" );
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document.write( "Now for the question:\r\n" );
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document.write( "Why is \"m\" used to represent the slope in a linear equation?\r\n" );
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document.write( "From this site:\r\n" );
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document.write( "http://www.numericana.com/answer/trivia.htm#slope\r\n" );
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document.write( "we read: \r\n" );
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document.write( "Well, the explanation is certainly not the one most often given, namely\r\n" );
document.write( "that \"m\" is the first letter of the French verb \"monter\", meaning \"to climb\"; I\r\n" );
document.write( "happen to know first-hand that virtually all French textbooks quote the generic\r\n" );
document.write( "linear function as y = ax+b.  If the tradition was of French origin, wouldn't\r\n" );
document.write( "the French use it? \r\n" );
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document.write( "In an earlier forum on this [apparently popular] subject, John H. Conway\r\n" );
document.write( "rightly called the above explanation an \"urban legend\".  He half-heartedly put\r\n" );
document.write( "forward [and later half-heartedly recanted] the theory that what we now\r\n" );
document.write( "call \"slope\" was once better known as \"modulus of slope\" (\"modulus of...\" has\r\n" );
document.write( "often been used to mean \"the parameter which determines...\").  In 1990, Fred\r\n" );
document.write( "Rickey (of Bowling Green University, OH) could not even find any use before\r\n" );
document.write( "1850 of the word \"slope\" itself to denote the tangent of a line's\r\n" );
document.write( "inclination... \r\n" );
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document.write( "Conway \"seemed to recall\" that Euler (1707-1783) did use m for slope, which\r\n" );
document.write( "remains unconfirmed.  However, Dr. Sandro Caparrini (University of Torino)\r\n" );
document.write( "found out that at least one contemporary of Euler did so, since Vincenzo\r\n" );
document.write( "Riccati (1707-1775) used the notation y = mx+n as early as 1757, in a reference\r\n" );
document.write( "to Jakob Hermann (1678-1733).  (This and other related facts have been reported\r\n" );
document.write( "online in the excellent historical glossary of Jeff Miller; look under Slope.) \r\n" );
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document.write( "Eric Weisstein reports that the use of the symbol m for a slope was popularized\r\n" );
document.write( "around 1844 [A Treatise on Plane Co-Ordinate Geometry, by M. O'Brien. \r\n" );
document.write( "Deightons (Cambridge, UK) 1844] and subsequently through several editions of a\r\n" );
document.write( "popular treatise by Todhunter, whose notation was y = mx+c. [Treatise on Plane\r\n" );
document.write( "Co-Ordinate Geometry as Applied to the Straight Line and the Conic Sections by\r\n" );
document.write( "I. Todhunter, Macmillan (London, UK) 1888]. \r\n" );
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document.write( "The preferred notation for the slope-intercept cartesian equation of a straight\r\n" );
document.write( "line in the plane is not at all universal, though.  Here's what we have gleaned\r\n" );
document.write( "so far.  \r\n" );
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document.write( "y = mx + n,  Vincenzo Riccati (1757)\r\n" );
document.write( "Netherlands, Uruguay \r\n" );
document.write( "y = mx + c,  UK \r\n" );
document.write( "y = mx + b,  US, Canada \r\n" );
document.write( "y = ax + b,  France, Netherlands, Uruguay \r\n" );
document.write( "y = kx + b,  Russia \r\n" );
document.write( "y = kx + m,  Sweden \r\n" );
document.write( "y = kx + d,  Austria \r\n" );
document.write( "y = px + q,  Netherlands (who also use both y = ax + b and y = mx + n)\r\n" );
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document.write( "Edwin
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