Sec5.1&5.2ClassNotes.notebook
April 22, 2014
Date:
5.1/5.2 Direct and Partial Variation
Example A school cafeteria charges $0.50 for an apple. Complete the table of values for n, the number of apples purchased, and C, the cost in dollars for a student who buys an apple each school day. Then graph the data from the table of values. Write an equation to represent the relation.
n
C
0
1
2
3
4
1
Sec5.1&5.2ClassNotes.notebook
April 22, 2014
This type of relation is an example of direct variation.
A direct variation has an equation of the form The graph of a direct variation is a straight line that passes through the In a direct variation, the ratio of corresponding values of the variable is
and is called the
Example Determine the constant of variation.
a) During the day, shadow lengths of trees vary directly with the height of the tree. A tree, 10m in height casts a shadow 15m long.
b) The amount collected for a walk­a­thon varies directly with the number of kilometres walked. Renee walked 25 km and collected $50.
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Sec5.1&5.2ClassNotes.notebook
April 22, 2014
Example To fix a car, Sally's Garage charges a flat fee of $20, plus $10/h. Complete this table of values for h, the number of hours of a repair job, and C, the cost in dollars. Then, graph the data from the table of values. Write an equation to represent the relation.
h
C
0
1
2
3
4
3
Sec5.1&5.2ClassNotes.notebook
April 22, 2014
This type of relation is an example of partial variation.
A partial variation has an equation of the form where b represents the m represents the
and The graph of a partial variation is a straight line that does pass through the origin.
Summary
Direct
Variation
Partial
Variation
y
y = mx + b
y = kx
(0, 0)
y
(0, b)
x
x
4
Sec5.1&5.2ClassNotes.notebook
April 22, 2014
Example Write the equation for each variation.
a) The cost to fix the furnace is a flat fee of $100, plus $60/h.
b) The charge to mow the lawn is $15 per hour.
c) Six chairs are made per day.
d) The moving charge is $450 to rent the truck and $50 per hour.
5
Sec5.1&5.2ClassNotes.notebook
April 22, 2014
Example Complete the table of values given that y varies partially with x. Identify the initial value of y and the constant of variation. Write an equation relating x and y.
x
y
0
2
1
7
2
3
17
4
37
Homework p.242 ­ 243 #1, 3, 5, 6
p.250 ­ 251 #1, 3, 4, 5, 6
6
Sec5.1&5.2ClassNotes.notebook
April 22, 2014
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