Linear vs. Nonlinear Functions
Grade 8 · Math · Functions · Montana, USA
Lesson Summary
Tell the difference between functions that make straight lines and those that make curves.
Explanation
A linear function has a constant rate of change and graphs as a straight line. Its equation can be written in the form y = mx + b. A nonlinear function has a rate of change that varies, producing a curve. For example, y = x² is nonlinear because the outputs don't increase by the same amount each time x goes up by 1. Checking a table for a constant difference in outputs is a quick way to test linearity.
Practice Questions
Q1: Is y = 5x − 3 linear or nonlinear?
Answer: Linear, because it is in the form y = mx + b with a constant rate of change of 5.
Q2: A table shows x = 1, 2, 3, 4 and y = 1, 4, 9, 16. Is this linear or nonlinear?
Answer: Nonlinear. The differences in y are 3, 5, 7, which are not constant. The rule is y = x².
Q3: How can you tell from a graph whether a function is linear?
Answer: If the graph is a perfectly straight line, the function is linear. If it curves at any point, it is nonlinear.
People Also Ask
What is Linear vs. Nonlinear Functions in Grade 8 Math?+
Linear vs. Nonlinear Functions is a lesson in the Functions chapter of Grade 8 Math. It is part of the Montana, USA school curriculum and covers key concepts that students need to understand at this level.
What grade level covers Linear vs. Nonlinear Functions?+
Linear vs. Nonlinear Functions is taught in Grade 8 as part of the Math curriculum in Montana, USA.
How can I help my child with Functions in Math?+
Start with the lesson summary and explanation on this page. Practice the questions provided, then use TutorTom for personalized, step-by-step help with Functions topics.