Does the data in the table represent a direct or inverse variation? Write an equation that models the data in the table. X | 1 | 3 | 5 | 10

Y | 4 | 12| 20| 40
A) direct variation y=4x
B) direct variation y=1/4x
C) inverse variation xy=4
D) inverse variation xy= 1/4
Pls help lol im really stuck on this question.

looks like when I multiply each of the x values by 4, I get the y value, mmmhhh?

so, clearly, y = 4x

direct variation is y = kx

Yes i see that too but i’m unsure of the type of variation.

Ah okay thank you

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

Let's calculate the ratios:

For x = 1, y = 4. Ratio = y/x = 4/1 = 4.
For x = 3, y = 12. Ratio = y/x = 12/3 = 4.
For x = 5, y = 20. Ratio = y/x = 20/5 = 4.
For x = 10, y = 40. Ratio = y/x = 40/10 = 4.

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

Now, let's determine the equation that models the data. In a direct variation, the equation takes the form y = kx, where k is the constant of variation.

Using any of the pairs of x and y values, we can find k by dividing y by x.

For example, using the pair (1, 4):
4 = k * 1
k = 4

So, the equation that models the data in the table is y = 4x.

Therefore, the correct answer is A) direct variation y = 4x.