Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer.

Question

x 5 10 15 20
y 2 1 StartFraction 2 over 3 EndFraction StartFraction 1 over 2 EndFraction

Answer 1

The relation in the table does not represent direct or inverse variation. This can be determined by comparing the ratio of y to x.

When x = 5, y = 2. Therefore, y/x = 2/5.
When x = 10, y = 1. Therefore, y/x = 1/10.
When x = 15, y = 2/3. Therefore, y/x = 2/15.
When x = 20, y = 1/2. Therefore, y/x = 1/20.

Since the ratios of y to x are not constant, this relation does not represent direct or inverse variation. Consequently, there is no equation to represent this relation.