Identifying Linear vs. Nonlinear Functions from Equations
Grade 8 math students learn to identify linear versus nonlinear functions from their equations. A function is linear if it can be written in y = mx + b form, while equations with x^2, exponent variables, or square roots represent nonlinear functions whose graphs are not straight lines. Covered in Big Ideas Math, Course 3, Chapter 6: Functions.
Key Concepts
A function is linear if its equation can be written in the form $y = mx + b$. If an equation cannot be written in this form, it represents a nonlinear function.
Common Questions
How do you identify a linear function from an equation?
A function is linear if its equation can be written in y = mx + b form. If the equation has terms like x^2, x in an exponent, or the variable under a square root, it represents a nonlinear function.
What makes a function nonlinear?
A function is nonlinear if its equation cannot be written as y = mx + b. Equations with squared variables like y = x^2 + 3 or exponential terms like y = 2^x are nonlinear.
What is the difference between linear and nonlinear functions?
Linear functions have constant rates of change and form straight-line graphs, expressed as y = mx + b. Nonlinear functions have varying rates of change and form curved graphs.
Which textbook covers linear vs nonlinear functions for Grade 8?
This topic is in Big Ideas Math, Course 3, Chapter 6: Functions.
What grade level covers linear and nonlinear functions?
Identifying linear versus nonlinear functions is typically covered in Grade 8 math.