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A linear equation is always a polynomial of degree 1 (for example x+2y+3=0). In the two dimensional case, they always form lines; in other dimensions, they might also form planes, points, or hyperplanes. Their "shape" is always perfectly straight, with no curves of any kind. This is why we call them linear equations.
Every other equation is nonlinear. Higher degree polynomials are nonlinear. Trigonometric functions (like sin or cos) are nonlinear. Square roots are nonlinear. The main exception is if the nonlinear piece can evaluate to a constant--for example, sqrt(4)*x is linear because sqrt(4) is just 2, and 2x is linear.
Linear equations have some useful properties, mostly in that they are very easy to manipulate and solve. Although they are quite limited in what they can represent, it is often useful to try and approximate complicated systems using linear equations so that they will be easier to think about and deal with.
Nonlinear equations, for the most part, are much harder to solve and manipulate. Sometimes you need them--nature doesn't always work in straight lines, and nor do mathematicians--but generally speaking, you can only solve nonlinear equations if the systems are fairly small and simple. Solving a linear system with a million interacting variables is very doable with a computer, and most nonlinear solvers aren't going to get even close to that.
where is the straight line in the ram ?