The Core Difference: Constant vs. Variable Change
The core difference between constant and variable rates of change is a Grade 7 functions concept in Big Ideas Math Advanced 2, Chapter 6: Functions. A linear function has a constant rate of change and graphs as a straight line in the form y equals mx plus b, while a nonlinear function has a variable rate of change and graphs as a curve. Nonlinear indicators include squared variables, cubed variables, variables in denominators, or variables as exponents.
Key Concepts
Property The core difference between these two types of functions lies in their rate of change:.
Linear Function: Has a constant rate of change (a steady slope). Its equation can always be written in the form $y = mx + b$, and its graph is a straight line.
Nonlinear Function: Has a variable rate of change (the steepness keeps changing). Its equation cannot be written as $y = mx + b$, and its graph forms a curve.
Common Questions
What is the difference between linear and nonlinear functions?
A linear function has a constant rate of change and its graph is a straight line. A nonlinear function has a variable rate of change and its graph is a curve. Nonlinear functions cannot be written in the form y equals mx plus b.
How do you identify a nonlinear function from its equation?
Look for variables raised to powers other than 1, such as x squared, x cubed, or variables in denominators or as exponents. Any of these indicate a nonlinear function.
What is a constant rate of change?
A constant rate of change means the output increases or decreases by the same amount for each unit change in the input, creating a straight-line graph. This is the defining feature of linear functions.
What textbook covers linear versus nonlinear functions in Grade 7?
Big Ideas Math Advanced 2, Chapter 6: Functions covers the core differences between linear and nonlinear functions with real-world examples.