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To Be or Not To Be a Linear Equation: That Is the Question

Determining whether an equation is linear or non-linear is helpful in graphing and in finding the characteristics of the given equation. In this subtopic we will determine whether a given equation is linear or non-linear, introduce the standard form of an equation of a line, determine how to find the x-intercept and y-intercept of a linear equation, and then use the intercepts to graph the equations of lines.

Important definitions include those for:

• linear equation
• non-linear equation
• standard form of an equation of a line
• x-intercept
• y-intercept

In this subtopic, we begin with lecture notes for use by the instructor with students or as an individual student activity. In the lecture notes, we define important terms, determine whether a given equation is linear or non-linear, introduce the standard form of an equation of a line, determine how to find the x-intercept and y-intercept of a linear equation, and then use the intercepts to graph the equations of lines. Elements within the lecture notes may be used to assess understanding of the content.

Activity two, Linear or Non-Linear Paper Strip Activity, is designed to use in the classroom and encourages students to become involved in the learning process. At the conclusion of the activity, students should be proficient in determining whether an equation is linear or non-linear and provide an explanation for their choice.

Activity three, Linear or Non-Linear…You Decide Activity, can be used as a take-home assignment for students or as an in-class quiz to determine understanding of linear and non-linear equations.

In the summary, instructors are provided with a Pre-Test and Post-Test of the subtopic. Instructors may choose to use both tests, or only the Post-Test as a final assessment.