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. x5101520y21StartFraction 2 over 3 EndFractionStartFraction 1 over 2 EndFraction
The relation in the table represents inverse variation. This is because as x increases, y decreases.
To write the equation representing the inverse variation, we can use the formula y = k/x, where k is the constant of variation.
Using the given values from the table, we can see that when x = 10, y = 2/3. Therefore, we can write:
2/3 = k/10
k = 2/3 * 10
k = 20/3
So the equation representing the relation is:
y = (20/3)/x
y = 20/(3x)