Is It Linear? Discovering Straight-Line Functions
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.
What Students Will Do
Students analyze multiple functions by:
- Filling in tables of values
- Observing how points are plotted on a graph
- Identifying whether the graph is a straight line or curved
- Checking for a constant rate of change
- Classifying each function as linear or non-linear
- Finding the slope and y-intercept of linear functions
- Explaining why non-linear functions do not meet the criteria
Functions Included
The worksheet includes a mix of:
- Linear functions (positive and negative slopes)
- Quadratic functions
- Cubic functions
This variety helps students see that not all non-linear functions behave the same way.
Skills & Standards Covered
- Interpret equations of the form y = mx+ b
- Recognize that linear functions graph as straight lines
- Identify constant vs changing rates of change
- Compare linear and non-linear growth patterns
- Explain why a function is or is not linear
Aligned to CCSS: 8.F.A.3
Why Teachers Love This Worksheet
- Strong focus on conceptual understanding
- Immediate visual feedback through live graphing
- Encourages reasoning, not just answers
- Includes both increasing and decreasing linear functions
- Clear, repeatable structure builds confidence
- Supports randomization, giving each student unique functions
- Works well for classwork, homework, or formative assessment
Learning Objective
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.
Randomization Available
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.
