Given the poor quality of this browser, it is difficult to illustrate the example sensibly but here is the best that I can do.
The general form is Ly = f(x) where L is a linear operator, y is the unknown function of x, and f is the given function.
L is of the form dny/dxn + g1(x)*dn-1y/dxn-1 + ... + gn-1(x)*dy/dx + gn(x)*y
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y = mx + b
A standard form of a linear equation would be: ax + by = c
The most general form of a linear equation, in n-dimentional space, is y = sum(mixi) + c where the summation is over i = 1,2,3,...,n-1 The simpler (2-dimensional) version of the linear equation is y = mx + c where m is the slope and c is the y-intercept.
aX+bY+cZ=0 Is a type of linear equation.
There is one form of linear equation that is not a function, and that is when x = c, where c is a constant.