Difference between Linear and Nonlinear Equation

The key difference between linear and nonlinear equations is that linear equations have a straight-line graph with a constant slope and a unique solution, while nonlinear equations have a curved graph with a varying slope and one or more solutions.

Linear Equation VS Nonlinear Equation

Characteristics	Linear Equations	Nonlinear Equations
Highest power of variable	1	Greater than 1
Graph shape	Straight line	Curved
Slope	Constant	Varies
Number of solutions	Unique	One or more
Form	Simple	More complex
Examples	2x + 3 = 0, 5y – 7 = 0, 3z + 1 = 0	x^2 + 3x – 2 = 0, y^3 – 2y + 1 = 0, z^(1/2) + z^(1/3) – 1 = 0

Difference between Linear and Nonlinear Equation

Linear Equations

1. Form a straight line or represent the equation for the straight line
2. Have only one degree, with the maximum degree being 1
3. All equations form a straight line in the XY plane, which can be extended in a straight form to any direction `
4. General Representation: y = mx + c, where x and y are variables, m is the slope of the line, and c is a constant value
5. Examples: 10x = 1, 9y + x + 2 = 0, 4y = 3x, 99x + 12 = 23y

Nonlinear Equations

1. Do not form a straight line but form a curve
2. Have a degree of 2 or more, but not less than 2
3. Form a curve, with the curvature of the graph increasing as the degree increases
4. General Representation: ax^2 + by^2 = c, where x and y are variables, and a, b, and c are constant values
5. Examples: x^2 + y^2 = 1, x^2 + 12xy + y^2 = 0, x^2 + x + 2 = 25 in a number form