Direct and Partial Variations
Direct Variation
Partial Variation
Compare the graphs on the right and left.
What is similar in each of the graphs on the left?
What is similar in each of the graphs on the right?
For each of the below graphs, identify the initial value or fixed cost.
Initial Value: ________
Initial Value: ________
Initial Value:___________
Summary:
Direct Variation
Partial Variation
6
Modeling Direct Variations
A telephone company offers a plan that
charges $0.12 per minute for long-distance
calls within Canada.
a) Complete the table of values for the longdistance plan.
Duration of
Call, t(mins)
Cost, C ( $)
0
5
10
b) Complete the first differences.
15
c) What type of relationship exists? Explain.
20
25
30
35
40
d) Make a graph of the data
e) Find the rate of change.
Cost
($)
f) Where does the line cross the
dependent axis? What does this point
mean?
g) Write an equation to model the cost
of long-distance calls with this plan.
Duration of Call (min)
h) Find the cost of a long distance call that lasts
32 mins using the graph
i) Find the cost of a long distance call that
lasts 60 mins using the equation.
j) Which method do you think is more accurate: the graph or the equation? Explain.
7
Modeling Partial Variations
A soccer league holds an awards banquet at the end of the season. The banquet hall charges $42 per
person for the meal plus $500 for the use of the hall.
a) Complete the table of values for the
banquet costs.
Number of
People, n
Banquet Cost, C ( $)
0
b) Complete the first differences.
25
c) What type of relationship do we have?
Explain
50
75
100
d) Make a graph of the data
125
e) Find the rate of change.
Cost
($)
f) Where does the line cross the
dependent axis? What does this
mean?
point
g) Write an equation to model the
cost of a banquet.
Number of People
h) Use the equation to find the cost of a banquet
for 60 people
i) Using the equation find the cost of a
banquet with 220 people.
8