Linear or Nonlinear From Tables, Constant Differences
Written by Adi Ackerman, Head Teacher
"Linear or Nonlinear From Tables, Constant Differences" is written for 8th Grade (Ages 13-14), and it covers Common Core 8.F.A.3. A 7th grader who is already steady on functions can use it too, and an older student can use it as a short review.
8th grade math worksheet: write the change in y between rows of eight tables and circle Linear when every change is equal. Answer key included. Part of our linear and nonlinear functions collection. Aligned to Common Core standards.
How do I use this worksheet?
Begin with graphs and equations, then move to tables with even steps before uneven ones. Use the context graphs and the card sort to finish.
What students will practice
- Students will find the change in y from each row to the next.
- Students will decide that equal changes mean a linear function.
- Students will classify eight tables as Linear or Nonlinear.
What Makes a Relation a Function
Functions From Sets of Ordered Pairs
Functions From Input-Output Tables
Is the Relation a Function? Mapping Diagrams
Functions From Graphs, Vertical Line Test
Check for Functions in Five Forms
Linear or Nonlinear From Graphs and Equations
Linear or Nonlinear Tables With Uneven Inputs
Curriculum Links
Common Core State Standards
Functions · 8th Grade
Standard: 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.
View all 8.F.A.3 worksheets →Find this in the curriculum
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FAQ
How do I use this linear and nonlinear functions worksheet?
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Begin with graphs and equations, then move to tables with even steps before uneven ones. Use the context graphs and the card sort to finish.
What does this worksheet teach?
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Write the change in y between rows of eight tables and circle Linear when every change is equal. The directions on the page read: Write the change in y from each row to the next in the blanks. Circle Linear if all the changes are equal. Otherwise circle Nonlinear. An answer key is included.
Can I use this linear and nonlinear functions worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade functions, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
How do you tell if an equation is linear?
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A linear equation can be written as y = mx + b. Equations with x squared, x times y or x in a denominator are nonlinear. Linear or Nonlinear From Equations asks students to rewrite each linear one as y = mx + b.
What if the x values in a table skip unevenly?
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Compare the rate of change, the change in y divided by the change in x, not just the change in y. Linear or Nonlinear Tables With Uneven Inputs practices this.
What does a curved graph say about a situation?
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The rate of change is not constant, so the quantity speeds up or slows down. Linear or Nonlinear Graphs in Context asks students to explain this for sample data such as a cooling cup of cocoa.
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What Makes a Relation a Function
Functions From Sets of Ordered Pairs
Functions From Input-Output Tables
Is the Relation a Function? Mapping Diagrams
Functions From Graphs, Vertical Line Test
Check for Functions in Five Forms
Linear or Nonlinear From Graphs and Equations
Linear or Nonlinear Tables With Uneven Inputs