LESSON 2.03:Direct & Partial VariationMFM1P

DIRECT VARIATION

Example

1) The total cost of bananas varies directly with

the mass, in kilograms, bought. Bananas cost $1.50/kg.

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 ($)

Example Continued

b) Graph the Relationship

x

y

0… … … …

…

…

…

…

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

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           

   

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

PARTIAL VARIATION

Consider working at East Side Mario’s

You get paid $8.00 per hour.You also get paid a $20.00

shift gratuity.

Hours

1

Pay ($)

8

2 16 + 20 = 363 24 + 20 = 44

10 80 + 20 = 100

X 8

X 8X 8

X 8

+ 20 = 28

In Partial Variation, one variable equals a fixed multiple of the other, plus a constant value.

Written as an equation

P = 8h + 20

pay hours Initial amount

Variable part

Fixed part

Pay vs HoursP

H1 2 3 4 5 6

10

20

30

40

50

60

00

The graph is a straight line that does not pass through the origin.

A professional baseball player can make $3 000 000 per year plus $100 000 for every win.

P = 100 000 w + 3 000 000

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

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

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

Example Continued

b) Graph the Relationship

x

y

0… … … …

…

…

…

…

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

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.