How to Determine If an Equation Is a Linear Function Without Graphing?

How to Determine If an Equation Is a Linear Function Without Graphing
••• PhotographyFirm/iStock/GettyImages

A linear function creates a straight line when graphed on a coordinate plane. It is made up of terms separated by a plus or minus sign. To determine if an equation is a linear function without graphing, you will need to check to see if your function has the characteristics of a linear function. Linear functions are first-degree polynomials.

    Check that the y, or independent variable, is by itself on one side of the equation. If it is not, rearrange the equation so that it is. For example, given the equation 5y + 6x = 7, move the 6x term to the other side of the equation by subtracting it from both sides. This yields 5y = 7 - 6x. Then divide both side by 5 so you have y = 7/5 - (6/5)x.

    Determine whether the equation is a polynomial or not. For an equation to be a polynomial, the power of the independent or "x" variable of each term must be a whole number. The terms can be made up of constants and variables. If the equation is not a polynomial, it is not a linear equation. In the example, y = 7/5 - (6/5)x has one "x" term and its power is 1. Because 1 is a whole number, y = 7/5 - (6/5)x is a polynomial.

    Determine whether the equation is a first-degree polynomial. Locate the exponent with the highest degree out of the terms. That exponent is the degree of the polynomial. If it is one, it is a linear equation. Because the highest power of "x" in y = 7/5 - (6/5)x is 1, it is a linear function.


    • Make sure no variable is multiplied by another variable in the function. If that's the case, it's not a linear equation.

Related Articles

How to Find the Minimum or Maximum in a Quadratic Equation
How to Solve Binomial Equations by Factoring
How to Solve a Parabola
How to Factor Prime Trinomials
How to Factor Polynomials With 4 Terms
How to Solve Trinomials
How to Use Elimination to Solve the Linear Equation
What Is the Square Root Method?
The Foil Method With Fractions
How to Factor Higher Exponents
How to Identify Linear & Nonlinear Equations
How to Find Equations of Tangent Lines
How to Help With Polynomials
How to Find Half of a Fraction
How to Find The Slope of a Line Given Two Points
How to Simplify Exponents
Tricks for Factoring Quadratic Equations
Facts About Functions for Algebra 1
How to Identify a Numerical Coefficient of a Term
How to Solve for Both X & Y

Dont Go!

We Have More Great Sciencing Articles!