how do you know when to homogenise lines??????

Homogenization is intensive blending of mutually related substances or groups of mutually related substances to form a constant of different insoluble phases (sometimes with addition of surfactants) to obtain a suspension or emulsion.
The homogenization is the natural procedure to describe processes in complicated structures with known microstructures.

It allows to replace a highly inhomogeneous medium with an equivalent homogeneous material, to estimate the norm of fluctuations of fields, etc.

Homogenization reduces the original problem to a problem which is doable, and this simplified problem reflects most of important features of the original one.

So homogenising a curve with a st line means finding a straight line, which can be used to make up essential characteristics of the curve.
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linear combination of two curves
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if c1 and c2 are two curves, then the curve c3= a*c1+b*c2 is called as a linear combination of c1 and c2.

Significance of this combination is that characteristics of c3 has the characteristics of c1 as well as c2.