Students explore linear and non-linear functions by completing tables, observing graphs, and analyzing equations. They identify straight-line graphs, constant rates of change, and the structure of y=mx+b, then explain why other functions are not linear. Aligned to CCSS 8.F.A.3 and ideal for practice or assessment.
Help students clearly understand what makes a function linear or non-linear with this interactive, practice-focused worksheet aligned to Common Core 8.F.A.3. Students build understanding by completing tables, watching graphs form in real time, and connecting those visuals to the structure of each equation.
This activity moves beyond memorization and helps students discover why linear functions create straight-line graphs and why other functions do not.
Students analyze multiple functions by:
The worksheet includes a mix of:
This variety helps students see that not all non-linear functions behave the same way.
Aligned to CCSS: 8.F.A.3
Students will determine whether a function is linear or non-linear by analyzing its equation, table of values, and graph. They will interpret the structure of y=mx + b identify constant rates of change, and explain why functions that do not have a constant rate of change are not linear.
This worksheet supports randomization, meaning students may receive different linear and non-linear functions with different values. This encourages independent reasoning and prevents copying.
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
Interpret the equation *y = mx + b* as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. *For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line*.
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