Cogito
Grade 8 Math · Chapter 6 · Lesson 2
Linear and Nonlinear Functions
Straight, or something else.
10 problems · about 19 minutes · 8.F.A.3
What this lesson teaches
The child distinguishes linear from nonlinear functions using a graph, a table, or an equation.
- A linear function changes by the same amount for every equal step in x.
- Its graph is a straight line and its equation has the form y = mx + b.
- A changing rate of change means the function is not linear.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — What a Function Is: Rule "multiply by 4 then add 1". What comes out when 5 goes in?
Answer 21
Why 21.
Review — Solving a System by Elimination: x + y = 12 and x − y = 4. What is x?
Answer 8
Why x = 8.
Review — Solving a System by Substitution: y = 4x and x + y = 15. What is x?
Answer 3
Why x = 3.
Warm Up
Straightforward practice. Get the method working first.
3 problems4, 10, 16, 22. Constant rise?
Answer 6
Why 6, so it is linear.
2, 6, 10, 14. Constant rise?
Answer 4
Why 6 − 2.
Is y = 3x + 2 linear? 1 for yes, 0 for no.
Answer 1
Why It is mx + b.
Build It Up
The same ideas with more to keep track of.
2 problems1, 2, 4, 8. Is it linear? 1 for yes, 0 for no.
Answer 0
Why It doubles rather than adding.
10, 7, 4, 1. Constant rise?
Answer -3
Why It falls by 3.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Table: 5, 9, 13, 17. What is the constant rise?
Answer 4
Why 4, so it is linear.
The Curve: Is y = x² linear? 1 for yes, 0 for no.
Answer 0
Why No.