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
The relation in the table represents inverse variation. This is because as x increases, y decreases, and the product of x and y remains constant.
To represent the relation, we can write the equation y = k/x, where k is the constant of variation. To find k, we can pick any pair of x and y values from the table. Let's use the first pair (5, 2):
2 = k/5
2 * 5 = k
k = 10
Therefore, the equation representing the relation is y = 10/x.
This equation accurately represents the relationship between x and y in the table, showing that y is inversely proportional to x.