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 represents inverse variation. This can be determined by the fact that as x increases, y decreases.
To write an equation to represent the relation, we can use the formula for inverse variation: y = k/x, where k is a constant.
Plugging in the values from the table:
For x = 5, y = 2: 2 = k/5
For x = 10, y = 1: 1 = k/10
Solving for k, we get k = 10.
Therefore, the equation that represents the inverse variation in the table is y = 10/x.