The general form of a linear function
is:
f(x) = ax + b
If the equation can
be placed into this form, then it is linear. Otherwise, it is
not.
2x^2 is a quadratic (order 2) polynomial. Thus, 2x^2-1 is not
linear.
A linear function has the shape of a line. Higher order
polynomials have curves. This is another way to tell that the equation is not
linear.
Linear equations are special because it is easy to
interpolate the exact answer if you know two points on a line, and want to find a third point.
Because linear equations do not have variables that are products of one another, they are often
easy to solve. This makes them very useful in math and science.
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