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LESSON 2.03:Direct & Partial VariationMFM1P
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DIRECT VARIATION
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Example
1) The total cost of bananas varies directly with
the mass, in kilograms, bought. Bananas cost $1.50/kg.
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Example Continued
a) Choose appropriate letters for variables. Make a table of values showing the cost of 0kg, 1kg, 2kg, and 3kg of bananas.
Mass (kg) Cost ($)
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Example Continued
b) Graph the Relationship
x
y
0… … … …
…
…
…
…
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Write a RuleCost 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
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Bulk honey costs $7.50/kg.a) Complete a table to show the cost of honey for amounts from 1 kg to 5 kg.b) Graph the data. Does the graph represent direct variation? Explain.
Amount of honey (kg)
Cost ($)
0 1
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Remember…
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 = mx
0 x
y
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PARTIAL VARIATION
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Consider working at East Side Mario’s
You get paid $8.00 per hour.You also get paid a $20.00
shift gratuity.
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Hours
1
Pay ($)
8
2 16 + 20 = 363 24 + 20 = 44
10 80 + 20 = 100
X 8
X 8X 8
X 8
+ 20 = 28
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In Partial Variation, one variable equals a fixed multiple of the other, plus a constant value.
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Written as an equation
P = 8h + 20
pay hours Initial amount
Variable part
Fixed part
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Pay vs HoursP
H1 2 3 4 5 6
10
20
30
40
50
60
00
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The graph is a straight line that does not pass through the origin.
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A professional baseball player can make $3 000 000 per year plus $100 000 for every win.
P = 100 000 w + 3 000 000
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If he wins 15 games, how much will he make?
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
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Example
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 $1.25 for each kilometre you travel.
a) Fill in the table of values.
Distance (km)
Cost ($)
Independent Dependent
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Example
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 $1.25 for each kilometre you travel.
a) Fill in the table of values.
Distance (km)
Cost ($)
0 2.75
1 4.00
2 5.25
3 6.50
4 7.75
Independent Dependent
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Example Continued
b) Graph the Relationship
x
y
0… … … …
…
…
…
…
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x
y
0 1 2 3 4
1.50
3.00
4.50
6.00
7.50
9.00
Cost vs. Distance
Distance (km)
Cos
t ($
)
Example Continued
b) Graph the Relationship
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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.