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