What Is the Difference Between Linear and Nonlinear Equations?

The graph of a linear equation forms a straight line, while a non-linear equation's graph does not form a straight line.Most equations can be graphed on a Cartesian coordinate plane using the variables x and y.

An example of a linear equation is y=x+3. The graph of this equation is a straight line running parallel to the x-axis at y=3. Linear equations may produce lines of any slope or location, but they always produce straight lines.

An example of a non-linear equation is y=x^2+3. The graph of this equation does not produce a straight line. It produces a symmetrical u-shaped curve called a parabola with its lowest point at y=3. Parabolas can be positive or negative, and the steepness of the curve can vary greatly, but the same basic shape is always produced.

Linear equations produce straight lines because the degree of x is equal to one. The word degree here refers to the power or exponent of x. X raised to the first power, as in the first example, has a degree of one.

In the second example, x is raised to the second power, so x has a degree of two. If x is raised to any power except one, the equation is non-linear. Non-linear equations do not always produce parabolas, but they always produce curves.