Question

How can you tell if an equation is linear?

   How can you tell if an equation is linear?

Precalculus

Raymond A. Barnett,… 7th Edition

Chapter 1, Problem 3

Instant Answer

Solved by Expert Erika Bustos

07/17/2021

Step 1

A linear equation is an equation that forms a straight line when graphed. It has the general form of \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the y-intercept. Show more…

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How can you tell if an equation is linear?

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Key Concepts

Linear Equation

A linear equation is one where each term is either a constant or the product of a constant and a single variable, with no variables multiplied together or raised to any power other than one. This ensures that the equation represents a straight line when graphed.

Degree of Variables

The degree of an equation refers to the highest power of the variable(s) present. For an equation to be linear, each term involving a variable must have an exponent of one, distinguishing it from non?linear equations which involve higher powers.

Standard Form

Linear equations are often expressed in standard forms, such as y = mx + b or Ax + By = C, where m and b (or A, B, and C) are constants. Recognizing these forms helps in identifying the equation as linear since they clearly show that the variables are only to the first power.

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