# For the data in the table does Y very directly with X if it does right in equation for the direct variation

X|Y
10|12
15|18
20|24
A.yes:y=1.2x
B.yes:y=2x
C.yes:y=x+1
D.no:y does not vary directly with x

## 12/10 = 1.2

18/15 = 1.2
24/20 = 1.2

So what do you think??

## To determine if Y varies directly with X, we need to check if there is a constant ratio between the two variables. Let's calculate the ratio for each pair of X and Y values:

For the first pair (10, 12): 12/10 = 1.2
For the second pair (15, 18): 18/15 = 1.2
For the third pair (20, 24): 24/20 = 1.2

Since the ratio is the same (1.2) for all pairs, we can conclude that Y varies directly with X.

Therefore, the correct equation for the direct variation is:

A. yes: y = 1.2x

## To determine if Y varies directly with X, we need to check if the ratio between Y and X remains constant across all data points.

Let's calculate the ratio (Y/X) for each data point:
1) For X = 10 and Y = 12, the ratio (Y/X) = 12/10 = 1.2
2) For X = 15 and Y = 18, the ratio (Y/X) = 18/15 = 1.2
3) For X = 20 and Y = 24, the ratio (Y/X) = 24/20 = 1.2

Since the ratio (Y/X) is the same (1.2) for all data points, we can conclude that Y varies directly with X.

Now, let's find the equation for the direct variation, which is of the form y = kx. In this equation, 'k' represents the constant of variation.

We can use any of the data points to find 'k'. Let's use the first data point (X = 10, Y = 12):

12 = k * 10

To solve for 'k', divide both sides of the equation by 10:

k = 12/10 = 1.2

Therefore, the equation for direct variation is y = 1.2x.

So the correct answer is A. Yes, y = 1.2x.