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 2/3 1/2
The relation in the table does not represent direct nor inverse variation, as the values of y are not directly proportional or inversely proportional to the values of x.
To determine if it is direct or inverse variation, we can calculate the ratios of y to x for each pair of values:
y/x:
5/2 = 2.5
10/1 = 10
15/(2/3) = 22.5
20/(1/2) = 40
Since the ratios are not constant, the relation is neither direct nor inverse variation.
Therefore, there is no equation to represent the relation in this case.