What are the ways of finding the linear functions?

Answer 1

A linear function can be determined simply from its form. A linear function, over a set of variables, x1, x2, x3, etc is of the form

a1x1 + a2x2 + a3x3 + ... = b

where a1, a2, a3, etc and b are constants.

In graphical terms the linear function over n variables is a straight line in n-dimensional space.

In 2-d different letter are used instead of subscripts and the equation becomes ax + by = c

This can easily be shown to be equivalent to y = mx + c (though with a different value for c).