To determine if the relationship between the variables in the table is a direct variation, an inverse variation, or neither, we need to check if there is a constant ratio between x and y.
Let's calculate the ratios for the given values:
For x = 3, y = 15
3 / 15 = 0.2
For x = 8, y = 40
8 / 40 = 0.2
For x = 10, y = 50
10 / 50 = 0.2
For x = 22, y = 110
22 / 110 = 0.2
Since the ratio x / y is constant at 0.2, the relationship between the variables is a direct variation.
The function that models the direct variation relationship between x and y is:
y = kx
To find the value of k, we can choose any point from the table. Let's choose x = 3 and y = 15:
15 = k * 3
k = 15 / 3
k = 5
Therefore, the function that models the direct variation relationship between x and y is:
y = 5x
Note: Enter your answer and SHOW ALL THE STEPS NECESSARY to solve this problem in the space provided. You will not receive credit without all work shown. x 3 8 10 22 y 15 40 50 110 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.
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