How To Identify Linear & Nonlinear Equations

Equations are mathematical statements, often using variables, that express the equality of two algebraic expressions. Linear statements look like lines when they are graphed and have a constant slope. Nonlinear equations appear curved when graphed and do not have a constant slope. Several methods exist for determining whether an equation is linear or nonlinear, including graphing, solving an equation and making a table of values.

Step 1

Plot the equation as a graph if you have not been given a graph.

Step 2

Determine whether the line is straight or curved.

Step 3

If the line is straight, the equation is linear. If it is curved, it is a nonlinear equation.

Step 1

Simplify the equation as closely as possible to the form of y = mx + b.

Step 2

Check to see if your equation has exponents. If it has exponents, it is nonlinear.

Step 3

If your equation has no exponents, it is linear. "M" represents the slope.

Step 4

Graph the equation to check your work. If the line is curved, it is nonlinear. If it is straight, it is linear.

Step 1

Make a table of sample x values and solve for the resulting y values. Choose x values that are a constant numerical distance from each other. For example, put x values of -4, -2, 2 and 4 into the equation and solve for y for each value.

Step 2

Calculate the differences between the y values.

Step 3

If the differences are constant, or the same value, the equation is linear and has a constant slope. If the differences are not the same, the equation is not linear.