MPM1DI
Partial Variation
Example 1: A banquet hall charges a flat fee of $4000 for an event plus a charge of $100 per person attending.
Write a mathematical model to calculate the cost of an event. Does the cost of an event depend on the number of
people that attend the event?
Solution:
A partial variation has an equation of the form

m is the constant of variation

b is the initial value (fixed value)
, where m and b are constants, and
Note that when x = 0, y = initial value (not zero).
The graph of a partial variation does not pass through the origin.
Example 2: Represent the following relationship using a mathematical model. The cost of a gym
membership is $100 plus $30 per month.
a)
Identify your variables. Use Let statements.
b)
Which variable is the independent? dependent?
c)
Create a table of values, include at least 4 values.
MPM1DI
Partial Variation
d)
Graph the relationship. Include appropriate labels.
e)
What is the rate of change? What does it represent?
f)
What is the initial value? What does it represent?
g)
Write an equation to represent this relationship.
Example 3: The following tables represent the relationship between the cost, in dollars, and the number of
videos rented.
Identify the relation as being partial or direct. Justify your answer.
Vijay’s Video
x
y
# of videos
Cost ($)
0
0
1
5
2
10
Variation:
Homework: Pg. 250: #1, 2, 4, 6, 9, 10
Vanessa’s Video
x
y
# of videos
Cost ($)
0
4
1
6
2
8
Variation: