Determine If The Following Equation Is Linear Calculator

Use our calculator to quickly determine if an equation is linear. Learn the definition of linear equations, how to test them, and get step-by-step solutions.

What is a Linear Equation?

A linear equation is an equation that defines a straight line when graphed. It has the general form:

y = mx + b

Where:

y is the dependent variable
m is the slope of the line
x is the independent variable
b is the y-intercept

Linear equations have these key characteristics:

All variables are to the first power
No variables are multiplied together
No variables are in the denominator
No trigonometric, exponential, or logarithmic functions

How to Test if an Equation is Linear

To determine if an equation is linear, follow these steps:

Identify all variables in the equation
Check that all variables are to the first power
Verify there are no products of variables (like xy)
Ensure no variables are in denominators
Confirm there are no trigonometric, exponential, or logarithmic functions

Tip: If the equation can be rewritten in the form y = mx + b, it's linear. If not, it's nonlinear.

Examples of Linear and Non-Linear Equations

Linear Equations

y = 3x + 2
2x - 5y = 10
x + y = 7

Non-Linear Equations

y = x² + 3x + 2
xy = 5
y = 2x + 3/x
y = sin(x)

FAQ

What makes an equation nonlinear?

An equation is nonlinear if it contains variables raised to powers other than 1, products of variables, variables in denominators, or special functions like sine, cosine, or logarithms.

Can a system of equations be linear?

Yes, a system of equations is linear if each equation in the system is linear. For example, y = 2x + 1 and 3x - y = 4 form a linear system.

Are all straight lines linear equations?

Yes, any equation that graphs as a straight line is a linear equation, and it can be written in the form y = mx + b.