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 represents inverse variation.
To show this, we can calculate xy for each pair of values:
For x=5, y=2, xy=5*2=10
For x=10, y=1, xy=10*1=10
For x=15, y=2/3, xy=15*2/3=10
For x=20, y=1/2, xy=20*1/2=10
Since xy remains constant at 10 for all the pairs of x and y values, the relation is inversely proportional.
The equation that represents this inverse variation is: xy = k, where k is the constant of variation.
In this case, k=10, so the equation is xy = 10.