# Linear and Non-Linear Functions

These lessons, with videos, examples and step-by-step solutions help Grade 8 students learn how to interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Common Core: 8.F.3

### Suggested Learning Targets

• I can recognize that a linear function is graphed as a straight line represented as an equation in the form y = mx + b.
• I can recognize the equation y = mx + b is the equation of a function whose graph is a straight line where m is the slope and b is the y-intercept
• I can provide examples of nonlinear functions using multiple representations (tables, graphs, and equations).
• I can compare the characteristics of linear and nonlinear functions using various representations.

The following table shows how to represent functions using graphs, equations, verbal explanations, and tables. Scroll down the page for more examples and solutions.

Interpret the equation y = mx + b as defining a linear function (Common Core 8.F.3)
Linear v Non Linear Functions 1 (8.F.3)

How can you tell if a function is linear?

• Graph is a straight line.
• Equation can be written in the form y = mx + b

Examples of linear, exponential and quadratic functions.

8.F.3-1 - Linear vs. Non-Linear Functions

8.3 Representing linear functions

Linear or Non-Linear Functions

Non Linear Functions 8.F.3
In this common core example, we look at non linear functions through the structure of an equation, table and graph.

Linear & Nonlinear Functions
Identify functions using tables, graphs or equation.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.