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Section 9.1
INVERSE VARIATION
Solving Inverse Variation:
 Definition 1: A function in the form xy = k or
y = k/x, where k ≠ 0, is an inverse variation.
The constant of variation is k, the product x * y for
an ordered pair (x, y).
Example 1: Writing an Equation Given a Point:
a. Suppose y varies inversely with x and y = 7 when x
= 5. Write an equation for the inverse variation.
b. Suppose y varies inversely with x and y = 9 when x
= 2. Write an equation for the inverse variation.
Example 2: Finding the Missing Coordinate:
a) The points (3, 8) and (2, y) are two points on the
graph of an inverse variation. Find the missing
value.
b) The points (3, y) and (5, 9) are two points on the
graph of an inverse variation. Find the missing
value.
TOTD
 Suppose y varies inversely with x, and a point on the
graph of the equation is (8, 9). Write an equation for
the inverse variation.
 The points (5, 6) and (3, y) are two points on the
graph of an inverse variation. Find the missing value.
Example 3: Determining Direct or Inverse
Variation:
 Do the data in each table represent a direct variation
or an inverse variation? For each table, write an
equation to model the data.
x
y
2
5
4
10
10
25
Example 3: Direct Variations and Tables:
 Do the data in each table represent a direct variation
or an inverse variation? For each table, write an
equation to model the data.
x
y
5
20
10
10
25
4
Example 4: Real-World Problem Solving:
 Explain whether each situation represents a direct
variation or an inverse variation.
a.
b.
Carpooling: The cost of $20 worth of gasoline is split among
several people.
School Supplies: You buy several markers for 70¢ each.
Example 5: Relating to the Real World
 Zoology: The heart rates and life spans of most
mammals are inversely related. Write an equation to
model this inverse variation. Use your equation to
find the average life span of a cat (heart rate 126
beats/min).
Animal
Mouse
Rabbit
Lion
Horse
Heart rate Life Span
(beats/min)
(min)
634
1,576,800
158
6,307,200
76
13,140,000
63
15,768,000
Example 6: Continued
 A squirrel’s heart rate is 190 beats per minute.
Find its average life span.
 An elephant’s life span is about 70 years. Find its average
heart rate.
TOTD
 Explain whether each situation represents a direct
variation or an inverse variation.

You buy several souvenirs for $10 each.

The cost of a $25 birthday present is split among several
friends.