MSA 2.3
Name ____________________________________Period _______Score ____/5
Linear Relationships and Constant Rate of Change
A rate of change is a rate that describes how one quantity changes in relation to another.
In a linear relationship, the rate of change between any two quantities is the same. A
linear relationship has a constant rate of change. The constant rate of change is written
as the change in y over the change in x.
1. The student council asks for cost estimates for a skating party. The following tables
represent the costs from two skating companies: Rollaway Skates and Wheelie’s Skates
and Stuff.
Rollaway Skates Wheelie’s Skates and Stuff
Number
of People
(x)
Cost $
(y)
Number
of People
(x)
Cost $
(y)
0
$0
0
$100
1
$5
1
$103
2
$10
2
$106
3
$15
3
$109
4
$20
4
$112
5
$25
5
$115
6
$30
6
$118
For each company, is the relationship between number of people and cost linear?
If so, what is the constant rate of change? For each company, is the relationship
between number of people and cost proportional? If so, what is the constant of
proportionality (k)?
Graph the points from each table on the graphs below. Make sure to label the x and y-
axes as well as write in the proper scale on each graph.
Does the graph help you to determine if the relationships are linear or proportional?
Why?
