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