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.

Question

x 5 10 15 20
y 2 1 StartFraction 2 over 3 EndFraction StartFraction 1 over 2 EndFraction

Answer 1

The relation in the table does not represent direct or inverse variation because the ratio of y to x is not constant for all values of x and y.

Equation for the relation: y = (1/5)x

Explanation: By looking at the table, we can see that y is always 1/5 of x. This consistent ratio between x and y indicates a direct variation relationship, which is represented by the equation y = kx, where k is the constant of variation. In this case, k = 1/5.

Therefore, the relation in the table represents direct variation.