# Difference between Linear and Nonlinear Equation

May 13, 2023

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**

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

**Nonlinear Equations**

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

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