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

Teaching Notes 8.12: Identifying Direct and Indirect Variation

Direct variation and indirect variation are easily confused. The quotient of the coordinates are

constant in direct variation but the product of the coordinates are constant in indirect variation.

1. Explain that direct and indirect variation are functions that identify the wayx-and
   y-coordinates are related.


2. Offer this example of direct variation: If one movie ticket costs $8, then two tickets cost $16,
   three tickets cost $24, and so on. Each pair of numbers can be represented as an ordered pair,
   (x,y). (1, 8), (2, 16), (3, 24) The quotient
   y
   x

of each ordered pair is 8.

3. Offer this example of indirect variation: Suppose a DJ is hired to play at a community picnic
   (for entertainment only and not to make a profit for the picnic organizers). If the DJ charges
   $500 and 50 people attend the picnic, the cost is $10 per person. If 100 people attend, the
   cost is $5 per person. If 25 people attend, the cost is $20 per person. Each pair of numbers can
   be represented as an ordered pair. (50, 10), (100, 5), (25, 20) The productxyof each ordered
   pair is 500.


4. Discuss the information, formulas, and example on the worksheet with your students. Be
   sure to relate both formulas to the example.

EXTRA HELP:

Consider every ordered pair. For a direct variation, the quotient of every ordered pair is the same.

For an indirect variation, the product of every ordered pair is the same.

ANSWER KEY:

(1)Direct (2)Neither (3)Indirect (4)Direct (5)Direct (6)Indirect

------------------------------------------------------------------------------------------

(Challenge)Brittany is incorrect. The quotient

y

x

of the first two ordered pairs is−

1

2

but the

quotient

y

x

of the last ordered pair is

6

− 3

or−2.

------------------------------------------------------------------------------------------

296 THE ALGEBRA TEACHER’S GUIDE