What is a Linear Equation?
A straight line graph represents a linear equation.
A linear equation that has only one variable is known as a linear equation in one variable. If we have “x” as a variable, the standard form of a linear equation in one variable will be Ax + B = 0.
A linear equation that has two variables is known as a linear equation in two variables. If we have “x” and “y” as variables, the standard form of a linear equation in two variables will be Ax + By = C.
If we plot a linear equation on the coordinate plane, it will represent a straight line. From the term “linear equation”, we can guess that the graph could be a straight line.
Examples of linear equations are as follows:
- 4x + 5 = 0
- 9x – 7y + 13 = 0
What is a Nonlinear Equation?
When the graph of an equation is not a straight line, it is termed as a nonlinear equation.
Some examples of nonlinear equations:
- x\(^2\) + 5x + 6 = 0
- x\(^3\) + 6x\(^2\) – 7x -19 = 0
- x\(^2\) + 6y\(^2\) + 6 = 0
- 6x\(^2\) + y\(^3\) + 7x + 43y + 21 = 0
If we plot a nonlinear equation on the coordinate plane, it will represent a curve. These curves may be parabolic, exponential, a complete circle, and so on.
The Difference Between Linear and Nonlinear Equations
Linear Equations | Nonlinear Equations |
|---|---|
In the coordinate plane, we represent linear equations as straight lines. | In the coordinate plane, we represent nonlinear equations as curves. |
Examples of linear equations: \(\bullet\) \(x~+~y~=~4\) \(\bullet\) \(12x~-~7~=~0\) | Examples of nonlinear equations:
\(\bullet\) \(x^5 ~-~6x~+~4~=~0\) \(\bullet\) \(x^7 ~-~y^3~+~x~-~y~+~10~=~0\) |
Solved Linear Vs Non Linear Equation Examples
Example 1. Identify whether the given equations are linear or nonlinear.
A. y = 4x + 3
B. x\(^3\) + y + 3 = 0
C. x + xy + y = 0
D. 4x + 6y + 7z + 9w = 0
Solution :
A. y = 4x + 3
The exponents of x and y are 1.
So, the given equation is linear.
B. x\(^3\) + y + 3 = 0
The exponent of x is 3.
So, the given equation is nonlinear.
C. x + xy + y = 0
In xy, the sum of exponents: 1 + 1 = 2. The degree of the polynomial is 2.
So, the given equation is nonlinear.
D. 4x + 6y + 7z + 9w = 0
The exponents of x, y, z and w are 1.
So, the given equation is linear.
Example 2. Identify whether the graph represents a linear or a nonlinear equation.
Solution:
The given graph is in the form of a curve.
So, it is a graph of a nonlinear equation.
Example 3. Identify whether the graph is of linear or nonlinear equations.
Solution:
The given graph is in the form of a straight line.
So, it is a graph of a linear equation.
A linear equation can be graphed as a straight line on the coordinate plane.
A nonlinear equation can be graphed as a curve on a coordinate plane.
While graphing a nonlinear equation, we can observe a parabolic curve, an elliptical curve, circles, and so on.