SOLUTION: I have a question about the equation, "y=mx+b" Why is "m" the slope, and why is "b" the intercept? Please explain specifically. Thank you.

The x-coordinate of the x-intercept is labeled "a" and the y-coordinate of the
y-intercept was labeled "b". That was logical because "a" comes just before "b"
in the alphabet, just as "x" comes just before "y".  In olden days they used
the intercept form for the equation of a line instead of the slope-
intercept form,.  The intercept form of a line is:



where a is the x-coordinate of the x-intercept and b is the y-coordinate of the
y-intercept.  This is somewhat analogous to the equation for an ellipse



whose center is at the origin and whose x-intercepts are (±a,0) and whose y-intercepts are (0,±b).






The slope "m" of any slanted line can be defined in terms of the
intercepts by the equation .
 
Now for the question:

Why is "m" used to represent the slope in a linear equation?

From this site:

http://www.numericana.com/answer/trivia.htm#slope

we read: 

Well, the explanation is certainly not the one most often given, namely
that "m" is the first letter of the French verb "monter", meaning "to climb"; I
happen to know first-hand that virtually all French textbooks quote the generic
linear function as y = ax+b.  If the tradition was of French origin, wouldn't
the French use it? 

In an earlier forum on this [apparently popular] subject, John H. Conway
rightly called the above explanation an "urban legend".  He half-heartedly put
forward [and later half-heartedly recanted] the theory that what we now
call "slope" was once better known as "modulus of slope" ("modulus of..." has
often been used to mean "the parameter which determines...").  In 1990, Fred
Rickey (of Bowling Green University, OH) could not even find any use before
1850 of the word "slope" itself to denote the tangent of a line's
inclination... 

Conway "seemed to recall" that Euler (1707-1783) did use m for slope, which
remains unconfirmed.  However, Dr. Sandro Caparrini (University of Torino)
found out that at least one contemporary of Euler did so, since Vincenzo
Riccati (1707-1775) used the notation y = mx+n as early as 1757, in a reference
to Jakob Hermann (1678-1733).  (This and other related facts have been reported
online in the excellent historical glossary of Jeff Miller; look under Slope.) 

Eric Weisstein reports that the use of the symbol m for a slope was popularized
around 1844 [A Treatise on Plane Co-Ordinate Geometry, by M. O'Brien. 
Deightons (Cambridge, UK) 1844] and subsequently through several editions of a
popular treatise by Todhunter, whose notation was y = mx+c. [Treatise on Plane
Co-Ordinate Geometry as Applied to the Straight Line and the Conic Sections by
I. Todhunter, Macmillan (London, UK) 1888]. 

The preferred notation for the slope-intercept cartesian equation of a straight
line in the plane is not at all universal, though.  Here's what we have gleaned
so far.  

y = mx + n,  Vincenzo Riccati (1757)
Netherlands, Uruguay 
y = mx + c,  UK 
y = mx + b,  US, Canada 
y = ax + b,  France, Netherlands, Uruguay 
y = kx + b,  Russia 
y = kx + m,  Sweden 
y = kx + d,  Austria 
y = px + q,  Netherlands (who also use both y = ax + b and y = mx + n)

Edwin