Taking a break from traditional lecture-style learning, this lesson is exactly what teachers are looking for--teacher-guided, student-led, independent learning. Students READ a short description of linear vs. non-linear graphs and expressions, then sees examples worked out for them. They consider the pattern given in the examples, and then TRY some examples on their own.
This worksheet is not designed to take a long time to complete. It is designed to simplify a concept that many students often overthink, to give them the opportunity to figure out the concept "on their own," and to be a reference for students as the unit moves forward.
I often gave this activity as a homework assignment before beginning work on linear vs. non-linear graphs and expressions. This worked well because we didn't have to waste time on the basics in class--students came into the room knowing how to tell if a graph or expression was linear or not, and we were able to build on that immediately.