LESSON 2.03:
Direct & Partial Variation
MFM1P
1) The total cost of bananas varies directly
with
the mass, in kilograms, bought. Bananas
cost $1.50/kg.
a) Choose appropriate letters
Mass (kg) Cost ($)
for variables. Make a table
of values showing the cost of
0kg, 1kg, 2kg, and 3kg of
bananas.
b) Graph the Relationship
y
…
…
…
…
0
…
…
…
…
x
Cost of 30 bags of rice?
Cost of rice in $ = 5 x (# of bags)
We can use the rule to determine the cost of 30 bags.
Cost of 30 bags in $ = 5 x 30 = $150
Bulk honey costs $7.50/kg.
a) Complete a table to show the cost of honey for amounts from 1
kg to 5 kg.
b) Graph the data. Does the graph represent direct variation?
Explain.
Amount of
honey (kg)
0
1
Cost ($)
If two values are directly related, then
one is a multiple of the other. y = mx
The graph of a direct relationship is a
straight line that goes through the
origin (0,0).
y
y = mx
0
x
You get paid $8.00 per hour.
You also get paid a $20.00
shift gratuity.
Pay ($)
1X8
8 + 20 = 28
2X8
3X8
16 + 20 = 36
10 X 8
24 + 20 = 44
80 + 20 = 100
In Partial Variation,
one variable equals a
fixed multiple of the
other, plus a constant
value.
Variable
part
Fixed
part
P = 8h + 20
pay
hours
Initial
amount
P
60
50
40
30
20
10
0
0 1
2
3
H
4
5
6
The graph is a straight line
that does not pass through
the origin.
P = 100 000 w + 3 000 000
P = 100 000 w + 3 000 000
P = 100 000 (15) + 3 000 000
P = 1 500 000 + 3 000 000
P = 4 500 000
Independent
Dependent
When you take a taxi, you
Distance
are charged a fixed rate of
(km)
$2.75 as soon as you sit
down. Once you start
moving, you are charged an
additional $1.25 for each
kilometre you travel.
Cost ($)
a) Fill in the table of values.
When you take a taxi, you
are charged a fixed rate of
$2.75 as soon as you sit
down. Once you start
moving, you are charged an
additional $1.25 for each
kilometre you travel.
a) Fill in the table of values.
Independent
Dependent
Distance
(km)
0
Cost ($)
1
4.00
2
5.25
3
6.50
4
7.75
2.75
b) Graph the Relationship
y
…
…
…
…
0
…
…
…
…
x
b) Graph the Relationship
Cost vs. Distance
y
9.00
Cost ($)
7.50
6.00
4.50
3.00
1.50
0
1
2
3
Distance (km)
4
x
Direct Variation is a
relationship between two
variables that allows the
graph to pass through
the point (0,0), and has
an equation similar to the
following: y=4x , C=8.5t ,
D=25t
Partial Variation is a
relationship between two
variables that DOES
NOT pass through the
point (0,0), and has an
equation similar to the
following: y=3x+5 , C=
6.5t+15 , D=22n-5 ,
please note the
addition/subtraction term
at the end of the
equation.