Direct and Partial Variation
Investigation - With a partner complete the following:
1. Complete the table and graph below for each equation:
A) y  3x
x
-2
-1
0
1
2
y  3x  5
y
x
-2
-1
0
1
2
y
Compare the lines that you graphed. What do you notice?
_______________________________________________________________
B) y  4x
x
-2
-1
0
1
2
y  4x  3
y
x
-2
-1
0
1
2
y
Compare the lines that you graphed. What do you notice?
_____________________________________________________________
Conclusion
Direct Variation: A line that passes through _____________________.
Partial Variation: A line that _________________________________.
2. Circle all equations that represent partial variation.
a) y  5x  2
b) y  6x
c) y  7x  2
d) y 
3. Circle all graphs that represent direct variation.
b)
c)
a)
1
x
2
d)
4. Identify each table as direct or partial variation. Justify your response.
a)
b)
c)
d)
x
0
1
2
3
4
5
y
4
8
12
16
24
28
x
0
1
2
3
4
5
y
0
-3
-6
-9
-12
-15
Table
Direct Variation
Partial Variation
x
-2
-1
0
1
2
3
y
-3
1
5
9
13
17
Graph
x
-2
-1
0
1
2
3
y
10
5
0
-5
-10
-15
Equation
Homework:
A taxicab driver charges $2.50 plus $0.50/km for each trip.
a) What is the dependent variable (y)? ___________________________
b) What is the independent variable (x)? __________________________
c) Write the equation for this relationship. ___________
d) Make a table of values.
x
Y
Independent Variable
Dependent Variable
0
2
4
6
e) Graph this relation.
f)
Use the graph to predict the cost of a 5km trip.
____________
This is called __________________
g) Use the graph to predict the cost of an 8 km
trip. ____________
This is called __________________
h) Use the equation to check your answer
5 km trip
8 km trip
i)
On the graph, where is the fixed cost?
j)
Describe the graph.
The graph of a partial variation is a _________________ _____________ that _________
_________ the origin (0, 0).
Homework:
A piano instructor charges $20/h.
a) What is the dependent variable (y)? ___________________________
b) What is the independent variable (x)? __________________________
c) Write the equation for this relationship. _______________________
d) Make a table of values.
x
Y
Independent Variable
Dependent Variable
0
2
4
6
e) Graph this relation.
f)
Use the graph to predict the cost of a 5 hour
200
lesson. ____________
180
This is called __________________
160
140
g) Use the graph to predict the cost of a 7 hour
120
100
lesson. ____________
This is called __________________
80
60
h) Use the equation to check your answer
5 hour lesson
7 hour lesson
40
20
1
i)
2
3
4
5
6
7
8
9 10
Describe the graph.
The graph of a direct variation is a _________________ _____________ that _________
_________ the origin (0, 0).
Direct Variation
Partial Variation