Dynamic Activity

Direct and Inverse Variation

Lesson Vocabulary

• inverse variation
• constant of variation for an inverse variation

Take note Key Concept: Inverse Variation

An equation of the form xy = k or y = k x , y equals , k over x . comma  where k ≠ 0 , k not equal to 0 comma  is an inverse variation.

The constant of variation for an inverse variation is k, the product x ⋅ y x dot y  for an ordered pair (x, y) that satisfies the inverse variation.

Problem 1 Writing an Equation Given a Point

Suppose y varies inversely with x, and y = 8 when x = 3. What is an equation for the inverse variation?

x y = k Use the general form of an inverse variation . 3 ( 8 ) = k Substitute 3 for  x  and 8 for  y . 24 = k Simplify . x y = 24 Write an equation . Substitute  24  for  k  in  x y = k . table with 4 rows and 3 columns , row1 column 1 , x y , column 2 equals k , column 3 cap usethegeneralformofaninversevariation . . , row2 column 1 , 3 , open 8 close , column 2 equals k , column 3 cap substitute3for . x . and8for . y . , row3 column 1 , 24 , column 2 equals k , column 3 cap simplify , . , row4 column 1 , x y , column 2 equals 24 , column 3 cap writeanequation . .cap substitute . 24 , for , k , in , x y equals k . , end table

An equation for the inverse variation is xy = 24, or y = 24 x . y equals , 24 over x . .