Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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.
(2 points)
To determine if the relationship between the variables in the table is a direct variation, an inverse variation, or neither, we need to see if y is directly proportional, inversely proportional, or not proportional to x.
Let's first check if it is a direct variation:
To do this, we divide y by x for each pair of values:
9/3 = 3
27/9 = 3
39/13 = 3
60/20 = 3
Since the ratio y/x is constant (3) for all values, this indicates a direct variation.
To write a function to model a direct variation, we use the formula y = kx, where k is the constant of variation.
From the table, we can see that for a direct variation, k = 3.
So, the function that models this direct variation relationship is:
y = 3x.