LESSON 2.03: Direct & Partial Variation MFM1P

1) The total cost of bananas varies directly with the mass, in kilograms, bought. Bananas the mass, in kilograms, bought. Bananas cost $1.50/kg. cost $1.50/kg.

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 ($)

b) Graph the Relationship x y 0 ………… … … … …

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 $7.50/kg. a) Complete a table to show the cost of honey for amounts from 1 kg to 5 kg. b) Graph the data. Does the graph represent direct variation? Explain. Amount of honey (kg) Cost ($) 0 1

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 0x y

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

1 Pay ($) = = = 100 X = 28

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

P = 8h + 20 pay hoursInitial amount Variable part Fixed part

P H

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

P = w

P = w P = (15) P = P =

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

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

b) Graph the Relationship x y 0 ………… … … … …

x y Cost vs. Distance Distance (km) Cost ($) 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.