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Direct Variation
Section 1.9
Notes: Direct Variation
 When two variable quantities have a constant ratio,
their relationship is called a ________________.
 The constant ratio is called the _____________________.
 The constant of variation is also known as the
_____________________.
What is a Direct Variation?
 A special equation in the form: y = kx
 k is called the “constant of variation”; it is also the slope
of the equation
 The variables have a direct relationship; as one
increases/decreases, so does the other
 The graph of a direct variation always passes through the
origin
 Example: y = 3x
Determining a Direct
Variation
FROM EQUATIONS:
 Put equation into form (y = ) and determine if it fits the
pattern y = kx
Are these direct variations?
x
y=x
y = 2x – 1
y
2
3x = 5y
Notes: Determine a Direct
Variation
 Not all situations with a constant rate of change are
proportional relationships.
 Likewise, not all linear functions are direct variations.
Determining a Direct
Variation
FROM TABLES:
 Solve each ordered pair for k (k = y/x)
 If k is constant for each ordered pair, you have a
direct variation
Examples
X
Y
X
Y
-6
9
-2
1
1
-1.5
3
6
8
-12
8
-4
Graphing Direct Variations
 Always know 1 point on the line: (0,0)
 Use k (the slope) to get additional points
Examples: Determine whether each linear
relationship is a direct variation. If so, state the
constant of proportionality
1.
Pictures, x
3
4
5
Profit, y
24
32
40
Year, x
5
10
15
Height, y
12.5
25
37.5
Essential Question
 How can you
determine if a linear
relationship is a direct
variation from an
equation? A table? A
graph?
 _______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_________