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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 is a direct variation, an inverse variation, or neither, we need to check if the ratio of y to x is constant.
Calculating the ratios for each data point:
y/x = 9/3 = 3
y/x = 27/9 = 3
y/x = 39/13 = 3
y/x = 60/20 = 3
Since the ratio of y to x is constant at 3 for all data points, the relationship between the variables is a direct variation.
To write a function to model this direct variation, we can use the formula y = kx, where k is the constant of variation.
We can choose any data point to find the value of k. Let's use the first data point (3, 9):
9 = k(3)
k = 3
Therefore, the function that models the direct variation relationship between x and y is:
y = 3x