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Grade 8 · Functions · 8.F.A.3

Linear and Non-Linear Worksheets

Free, printable, and ready to teach: a practice worksheet, homework, an exit ticket, and an answer key with step-by-step solutions — plus lesson slides you can edit. No sign-up needed.

First page of the linear and non-linear practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

Step-by-step math videos on the Math With Mr DJ YouTube channel →

Key idea

Linear means a constant rate. Equal differences prove it only when the x-steps are equal too.

Sample problems

Is y = −3x + 8 linear?
x: 0,1,2,3 → y: 5,8,11,14. Linear?
x: 0,1,2,3 → y: 1,2,4,8. Linear?
x: 2,4,8 → y: 7,11,19. Linear? Show the rates.

Common mistakes to watch for

Said no because of the minus, or because no table was given.
Said yes because there is a clear pattern. A pattern in the differences is not a constant difference — growing by 2 each time is still growing.
Agreed with her. This is the misconception this whole skill is built around, and it is worth saying that her rule is USUALLY right rather than simply wrong — she has learned a reliable shortcut and met the case it does not cover.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.

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