Characteristics of Linear and Non-Linear Relations
Linear and non-linear relations can be identified
 from the shape of their graphs
 by calculating first differences
 by looking at its equation
A) Identifying Linear and Non-Linear Relations from Graphs
Examine each graph and classify the relation as linear or non-linear.
B) Identifying Linear and Non-Linear Relations Using First
Differences
For each relation
 calculate the first differences
 classify the relation as linear or non-linear
a)
Number
0
100
200
300
400
Cost ($)
250
300
350
400
450
b)
Cube Side-Length
(cm)
1
2
3
4
5
Cube Volume
(cm3)
1
8
27
64
125
C) Identifying Linear and Non-Linear Relations from Equations
For each equation, classify the relation as linear or non-linear.
a) y = 4x2
b) y = -3x + 5
c) y = 7x – 3x3
d) y = 2.5x + 8
D) Exploring Linear and Non-Linear Equations Using a Graphing
Calculator
1.
Graph each relation using a standard viewing window.
Examine the graphs and classify each one as either linear or non-linear.
a) y = 2x – 3
b) y = -3x
c) y = 0.5x + 4
d) y = x2
e) y = x3 + x + 3
f) y = x – 0.5x4 – 4
What feature seems to determine whether a relation will have a linear or nonlinear graph?
2. Predict whether the following relations will have linear or non-linear graphs.
Test your predictions by graphing each relation.
a) y = 3x2
b) y = 5x – 2
c) y = -2x
d) y = 3x – x3
e) y = 0.2x4
f) y = 0.6x + 3
Follow Up: Characteristics of Linear and Non-Linear Relations Worksheet