Identifying Linear vs. Nonlinear Functions from a Graph
A function is linear if its graph is a non-vertical straight line, meaning it has a constant rate of change. A function is nonlinear if its graph is a curve, meaning the rate of change varies. The graph of y = -x + 3 is a straight line (linear). The graph of y = x squared - 1 is a U-shaped parabola (nonlinear). This visual classification skill from enVision Mathematics, Grade 8, Chapter 3 is the starting point for distinguishing linear from nonlinear functions in 8th grade algebra.
Key Concepts
A function is linear if its graph is a non vertical straight line. A function is nonlinear if its graph is not a straight line (e.g., it is a curve).
Common Questions
How do I tell if a function is linear or nonlinear from its graph?
If the graph is a straight line, the function is linear. If the graph curves, the function is nonlinear.
Is y = 2x + 5 linear or nonlinear?
Linear. Its graph is a straight line with slope 2 and y-intercept 5.
Is y = x squared linear or nonlinear?
Nonlinear. Its graph is a U-shaped parabola, not a straight line.
What does a constant rate of change look like on a graph?
A constant rate of change produces a straight line. The line rises or falls by the same amount for every one-unit increase in x.
Can a nonlinear function look almost straight in a small region?
Yes. Some curves are nearly flat over a small range of values. But if the overall shape curves rather than being perfectly straight, the function is still nonlinear.
When do 8th graders learn to identify linear vs. nonlinear functions?
Chapter 3 of enVision Mathematics, Grade 8 covers this in the Use Functions to Model Relationships unit.