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
check to see whether y/x is the same for all the rows.
12/10 = 6/5 now do the others.
If they are all the same, then y = 6/5 x
To determine if Y varies directly with X, we can check if the ratio of Y to X remains constant. If the ratio is the same for all data points, then Y varies directly with X.
Let's calculate the ratio of Y to X for each data point:
For X = 10, Y = 12, the ratio is 12/10 = 1.2.
For X = 15, Y = 18, the ratio is 18/15 = 1.2.
For X = 20, Y = 24, the ratio is 24/20 = 1.2.
Since the ratio is the same (1.2) for all data points, we can say that Y varies directly with X.
Now, to write the equation for direct variation, we can use the formula:
Y = kX
where k is the constant of variation.
To find k, we can use any of the data points. Let's use the first data point (10, 12):
12 = k * 10
Solving for k, we divide both sides by 10:
k = 12/10 = 1.2
The equation for the direct variation is:
Y = 1.2X