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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 in the table is a direct variation, an inverse variation, or neither, we can check if the ratios of y to x are constant.
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 ratios of y to x are constant at 3 for all values in the table, the relationship is a direct variation.
To write a function to model the direct variation relationship, we can set up the equation as y = kx, where k is the constant of variation.
Using any pair of x and y values from the table, such as x = 3 and y = 9, we can solve for k:
9 = k * 3
k = 9/3
k = 3
Therefore, the function that models the direct variation relationship is y = 3x.