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x 3 9 13 20
y 9 27 39 60
State whether the relationship between the variables in the table is a direct variation, an inverse variation, or neither. If it is a direct or inverse variation, write a function to model it.

1 answer

To determine if the relationship between x and y is a direct variation, inverse variation, or neither, we need to check if the ratio y/x is constant for all pairs of values.

1st pair: 9/3 = 3
2nd pair: 27/9 = 3
3rd pair: 39/13 = 3
4th pair: 60/20 = 3

Since the ratio y/x is constant (3) for all pairs of values, the relationship between x and y is a direct variation.

To write the function that models this direct variation, we can express the ratio as a proportion:

y/x = 3

y = 3x

Therefore, the function that models the relationship between x and y in the table is y = 3x.