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 an inverse variation. This can be seen because as the value of x increases, the value of y decreases. Additionally, when x is multiplied by a certain value, y is divided by that same value.
To write the equation representing this inverse variation, we can use the formula for inverse variation: y = k/x, where k is a constant of variation.
Using the first pair of values in the table (x=5, y=2), we can solve for k:
2 = k/5
k = 10
Therefore, the equation representing the inverse variation is y = 10/x.