Linear vs Nonlinear Equations

Linear Equation

A linear equation is an equation where the highest exponent of the variable(s) is one. It is of the general form y = mx + c; here, x and y are variables, m is the slope, and c is the constant.

Examples:

• y = 2x + 3
• 3x + 5 = 11
• 2x – 7y = 4
• y = 4x – 9

NonLinear Equation

Nonlinear equations are equations that have the degree of a variable greater than 1. It involves equations with square roots, logarithms, or trigonometric expressions. 

The general form of a non-linear equation is ax² + by² = c; here, x and y are variables, and a, b, and c are constants. 

Examples:

• y = x² + 5 
• y = x² + 2x – 3
• x³ – 4x + 2 = 0
• y = sin x
• ${y=\sqrt{x}+5}$

Differences

The table below shows the key differences between a linear and a non-linear equation:

Graphing

The graph of a linear equation always forms a straight line.

In contrast, the graph of a nonlinear equation is curved. It often takes the shape of a parabola and hyperbola.