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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.
To determine if the relationship between the variables x and y in the table is a direct variation, an inverse variation, or neither, we need to check if y is directly proportional to x, inversely proportional to x, or neither.
First, we need to calculate the ratio y/x for each pair of values in the table:
For x = 3, y = 9: y/x = 9/3 = 3
For x = 9, y = 27: y/x = 27/9 = 3
For x = 13, y = 39: y/x = 39/13 ≈ 3
For x = 20, y = 60: y/x = 60/20 = 3
Since the ratio y/x is constant (equal to 3), it indicates that the relationship between the variables x and y is a direct variation.
Therefore, the function that models this direct variation is:
y = 3x