MPM1D
Name:________________________
5.2: Partial Variation
Investigate: Carolyn gets a job at the Rogers Centre selling programs. She is paid $20 per
game and she is given 50 cents for every program that she sells.
a) Create a table showing the pay she can expect for a game where the number of programs
that she sells varies from 0 to 100. Go up by increments of 10 programs in your table.
b) Identify the independent and dependent variable.
Independent variable ___________________
Dependent variable ____________________
c) Graph this relationship. Describe the shape of this graph.
d) Examine your table. What is her
pay for selling 0 programs? Where
does this information show on your
graph?
e) Write an equation to describe this relationship. Be
sure to define the variables with appropriate “Let”
statements.
f) Use the equation to determine the amount Caroline will
get paid if she sold 45 programs.
g) Consider the amount that Caroline gets paid to sell 10 programs: __________________
 What happens to her pay when the
amount of programs sold is doubled?
 What happens to her pay when the
number of programs sold is tripled?
MPM1D
Name:________________________
CONCLUSION
The relationship between pay and # of programs sold (in the investigation) is an example of
_______________ _____________. The pay per program represents the _____________ cost
a.k.a. the _____________ ____ ______________. The $10 represents the ____________ cost
a.k.a. the _____________ _______________.
In general, if 𝑦 ___________ ___________ with 𝑥, the equation is of the form:
___________________________ where 𝒎 is the ______________ _____ ______________
and 𝒃 is the __________ or __________ _______________.
On a graph, we know two variables vary partially if the points form a ______________ _________
and that line does ________ go through the _______________________.
Comparing Direct and Partial Variation
Direct Variation
Definition
Table of
Values
Graphs
Equations
Partial Variation
MPM1D
Name:________________________
5.2: Examples
1. Classify each graph as a direct variation, a partial variation, or neither. Justify your
answer.
a)
b)
c)
d)
2. Classify the following table of values as representing a direct variation, a partial variation,
or neither. Justify your answer.
a)
b)
c)
x
y
x
y
x
y
0
5
0
0
0
7
1
9
1
-10
1
10
2
12
2
-20
2
13
3
17
3
-30
3
16
4
20
4
-40
4
19
3. Classify each of the following equations as a direct variation, a partial variation, or neither.
Justify your answer.
a) 𝑦 = 3𝑥
b) 𝑑 = −2𝑡 + 1
c) 𝑦 = 3𝑥 2
4. For each of the linear relations in Questions 1, 2 and 3, identify the initial value.
MPM1D
Name:________________________
5. Answer the questions below for each of the following table of values.
x
y
x
y
x
y
0
5
0
23
0
-2
1
10
1
20
1
3
2
3
2
20
3
4
5
2
14
3
4
30
13
4
8
23
a) Complete each of the table of values given that it represents a partial variation.
b) Identify the initial value for each of the above partial variations.
c) By what amount are each of the y-values increasing or decreasing by as the x –values
increase by 1? This is your constant of variation (CoV)
d) Write an equation relating 𝑦 and 𝑥 in the form of 𝑦 = 𝑚𝑥 + 𝑏
Answers to #5
b)
Initial Value =
Initial Value =
Initial Value =
c)
CoV =
CoV =
CoV =
d)
Equation:
Equation:
Equation:
6. You want to rent several movies from Movies R Us. There are two available options:
Option A  $6 per every movie rental
Option B  $20 monthly membership fee and $2 per every movie rental
a) Graph both relations from 0 to 10 movie rentals.
b) Classify the options as direct or partial variation.
Option A:
Option B:
c) Write an equation for each option relating the Cost
(C) to the number of movie rentals (n).
Option A:
Option B:
d) Compare the two options by discussing which option
is cheaper based on the number of movie rentals.