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Bacle

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**"Non-linear Lines". How to Avoid Lying, without Confusing.**

Hi, everyone:

I will be teaching an intro course in Linear Algebra this Spring.

Problem I am having is that the definition of linear does not

apply to lines that do not go through the origin:

Let L:x-->ax+b

Then L(x+y)=ax+ay+b =/ L(x)+L(y)

similarly: L(cx)=acx+b =/ c(L(x))=cax+cb

Which is true only for c=0 . So lines are affine objects, carelessly described as linear,

as in 'linear equations'

So, how does one reasonably avoid bringing up the issue of affine vs. linear

and still not refer to a collection of equations

ax_i +b=0

as linear equations?