
Re: Is y = mx + b linear?
Posted:
May 15, 2000 1:23 PM


In article <8fo83o$mfm@mcmail.cis.McMaster.CA>, kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) writes:
> [...]
> :>> Is y(x) = mx + b a linear function? > > [...] > > Habits are hard to break: some people are so much in a hurry (or so they > think) that they tend to abbreviate, often to the detriment of clarity. > > The function that transforms x into m*x+b is called a "linear polynomial > function", to place it in the sequence "constant, linear, quadratic, > cubic, ...". It is a burden of tradition we have to live with, even if it > clashes with more recent conventions. Now some drop the word "polynomial" > and the corresponding context, and a misunderstanding arises.
The earliest usages of "linear" were surely geometrical: linear measure, etc. (W.W. Sawyer says that "straight line" comes from "stretched linen [thread]".)
The earliest usage of "linear" in algebra was presumably in the phrase "linear equation". And this got its name because (if it's in two variables) its graph is a straight line  whether through the origin or not.
So whilst, if one takes the current usage as given, the older usage is a "burden", one could take a more etymological point of view and blame the "burden" on those who changed the word's meaning.
From this point of view, the people who were in too much of a hurry, and who introduced the potential for confusion, were those who first abbreviated "homogeneous linear transformation" by omitting "homogeneous".
 Robert Hill

