How do you know weather a statistical model with a regression line is linear or non linear?

If the regression line can be manipulated to arrive at y = a + bx it is linear in x. The regression FORM is linear even with curves such as nth degree polynomials, y = ab^x, and y = ae^bx. (In other words, you still use linear regression to arrive at your constants) I've heard of non-linear regressions, but shudder at the thought of deriving or trying to apply one.