The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 8.12: IDENTIFYING DIRECT AND INDIRECT

VARIATION

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Direct and indirect variations are functions that show howx-coordinates andy-coordinates

are related. Use the formulas below to find if a relation is direct or indirect. (kis a constant.)

Direct variation:

y 1

x 1

=

y 2

x 2

Indirect variation: x 1 y 1 =x 2 y 2

1. To determine if a relation is a direct variation, find the quotient
   y
   x
   of each ordered pair. If
   the quotients of the ordered pairs are the same, the variation is direct.


2. To determine if a relation is an indirect variation, find the productxyof each ordered
   pair. If the products of the ordered pairs are the same, the variation is indirect.

EXAMPLE

State if the coordinates describe a direction variation, an indirect variation, or neither. (2, 5),

(−1,−10), (−4,−2.5)

Because

5

2

=

− 10

− 1

, the coordinatesdo notdescribe a direct variation.

Because 2 · 5 =−1(−10)=−4(− 2 .5)= 10 , the coordinates describe an indirect variation.

DIRECTIONS: Determine if the coordinates describe a direct variation, an indirect

variation, or neither.

1. (1, 2), (2, 4), (3, 6) 2. (2, 8), (1, 16), (−4, 4) 3. (6, 5), (5, 6), (−3,−10)


2. (2, 2), (4, 4), (8, 8) 5.

(

1

2

,2

)

, (2, 8), (−1,−4) 6. (4, 3),

(

3

4

,16

)

, (6, 2)

CHALLENGE:Brittany said that (−2, 1), (−4, 2), and (−3, 6) is a direct variation

because the quotient of each ordered pair is−

1

2

. Is she correct? Explain
your answer.

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©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.