LESSON
9.1
NAME _________________________________________________________ DATE ____________
Reteaching with Practice
For use with pages 534–539
GOAL
Write and use inverse variation models and joint variation models
VOCABULARY
Inverse variation is the relationship of two variables x and y if there is a
k
nonzero number k such that xy k, or y .
x
The nonzero constant k is called the constant of variation.
EXAMPLE 1
Lesson 9.1
Joint variation occurs when a quantity varies directly as the product of
two or more other quantities. For instance, if z kxy where k 0, then
z varies jointly with x and y.
Classifying Direct and Inverse Variation
Tell whether x and y show direct variation, inverse variation, or neither.
a. x y 12
b.
5
x
y
c. x y
2
SOLUTION
k
x
a. Because x y 12 cannot be rewritten in the form y kx or y ,
x y 12 shows neither type of variation.
5
x, you obtain xy 5.
y
5
5
When solving for y, the result is y , so x shows inverse
x
y
variation.
b. If you cross-multiply in the equation
y
2
c. If you cross-multiply in the equation x , you obtain y 2x, so
y
y
shows direct variation.
2
Exercises for Example 1
Tell whether x and y show direct variation, inverse variation,
or neither.
1. xy 8
EXAMPLE 2
2. y x 5
3. y x
2
4. x y
3
Writing an Inverse Variation Equation
1
The variables x and y vary inversely, and y 2 when x 6. Write an
equation that relates x and y, and find y when x 3.
Copyright © McDougal Littell Inc.
All rights reserved.
Algebra 2
Chapter 9 Resource Book
19
LESSON
9.1
CONTINUED
NAME _________________________________________________________ DATE ____________
Reteaching with Practice
For use with pages 534–539
SOLUTION
Use the general equation for inverse variation to find k, the constant of
variation.
Lesson 9.1
y
k
x
Write general equation for inverse variation.
1
for y and 6 for x.
2
1
k
2 6
Substitute
3k
Solve for k.
3
The inverse variation equation is y .
x
When x 3, the value of y is:
y
3
1.
3
Exercises for Example 2
The variables x and y vary inversely. Use the given values to
write an equation relating x and y. Then find y when x 4.
5. x 10, y 2
EXAMPLE 3
6. x 3, y 3
7. x 2, y 8
Writing a Joint Variation Model
The variable z varies jointly with x and the square of y. When x 10 and
y 9, z 135. Write an equation relating x, y, and z, then find z when
x 45 and y 8.
SOLUTION
z kxy2
Write an equation for joint variation.
135 k109
Substitute 135 for z, 10 for x, and 9 for y.
135 810k
Simplify.
2
1
6
k
Solve for k.
1
The joint variation equation is z 6xy2.
When x 45 and y 8:
z 164582 480.
Exercises for Example 3
The variable z varies jointly with x and y. Use the given
values to find an equation that relates the variables. Then
find z when x 2 and y 8.
8. x 4, y 3, z 24
20
Algebra 2
Chapter 9 Resource Book
9. x 8, y 54, z 144
1
10. x 1, y 8, z 4
Copyright © McDougal Littell Inc.
All rights reserved.