does the data in the table represent a direct variation? write an equation to model the data in the table. A. Indirect variation; y=4x. B. Indirect variation; y=1/4x. C. direct variation; y=4x. D. direct variation; y=1/4x.

Answer 1

To determine if the data in the table represents a direct variation, we need to check if the ratio of y to x remains constant.

Let's assume that the table is as follows:

x | y
1 | 4
2 | 8
3 | 12
4 | 16

For a direct variation, the ratio of y to x should remain constant. Let's check by calculating the ratio of y to x for the given data:

1. y/x = 4/1 = 4
2. y/x = 8/2 = 4
3. y/x = 12/3 = 4
4. y/x = 16/4 = 4

Since the ratio of y to x remains constant at 4, the data in the table represents a direct variation.

The equation that models the data in the table will have the form y = kx, where k is the constant of proportionality. To find k, we can choose any pair of x and y from the table. Let's use the first pair:

x = 1, y = 4

Substitute these values into the general equation:

4 = k*1
k = 4

Therefore, the equation that models the data in the table is:

y = 4x

C. direct variation; y = 4x.