**100 POINTS**I WILL MARK AS BRAINLIEST IF YOU GET IT CORRECT!
Do the data in this table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
X - 1 2 5 10
Y - 6 12 30 60
A. Direct variation; y=1/6x
B. Inverse variation; xy=6
C. Direct variation; y=6x
D. Inverse variation; xy=1/6

As we know:

Direct variation => y = k*x, k is constant ( y/x = k = constant)

Inverse variation => y = k/x, k is constant (y*x = k = constant)

X - 1 2 5 10

Y - 6 12 30 60

Check the first 2 pair of X, Y:

(the remaining pair of value would show the same tendency)

X1 x Y1 = 1 x 6 = 6

X2 x Y2 = 2 x 12 = 24

=> X x Y is not a constant

=> Not an inverse variation.

=> B and D is incorrect

Otherwise, we have:

Y1/X1 = 6/1 = 6

Y2/X2 = 12/2 = 6

=> Y/X = 6

=> A direct variation with k = 6

=> y = 6x

=> Option C is correct

Hope this helps!

:)

C. Direct variation; y = 6x

Step-by-step explanation:

Let's determine what direct and inverse variation are:

- Direct: y = kx, where k is any constant

- Inverse: y = k/x, where k is any constant

Here, let's look at the relationship between x and y. The first column is x = 1 and y = 6, so let's put that into y = kx and try:

y = kx

6 = k * 1

k = 6

Does this pattern continue? Check with the second column:

y = 6x

12 =? 6 * 2

12 = 12

This does work, and if you try all the other columns, they provide true statements, as well.

Thus, the answer is direct variation because y = 6x is of the form y = kx, and the equation is y = 6x because for every value of x, the y is 6 times that x value. The answer is C.

step-by-step explanation: