Dynamic Activity

Direct Variation

Lesson Vocabulary

• direct variation
• constant of variation for a direct variation

Problem 1 Identifying a Direct Variation

Does the equation represent a direct variation? If so, find the constant of variation.

1. 7 y = 2 x y = 2 7 x ← Solve each equation for  y . table with 2 rows and 2 columns , row1 column 1 , 7 y , column 2 equals 2 x , row2 column 1 , y , column 2 equals , 2 sevenths , x leftwards arrow . cap solveeachequationfor . y . , end table

   The equation has the form y = kx, so the equation is a direct variation. Its constant of variation is 2 7 . 2 sevenths , .

2. 3 y + 4 x = 8   3 y = 8 − 4 x ← Solve each equation for  y . y = 8 3 − 4 3 x   table with 3 rows and 3 columns , row1 column 1 , 3 y plus 4 x , column 2 equals 8 , column 3 , row2 column 1 , 3 y , column 2 equals 8 minus 4 x , column 3 leftwards arrow . cap solveeachequationfor . y . , row3 column 1 , y , column 2 equals , 8 thirds , minus , 4 thirds , x , column 3 , end table

   You cannot write the equation in the form y = kx. It is not a direct variation.

✓ Got It?

1. Does 4x + 5y = 0 represent a direct variation? If so, find the constant of variation.