To solve for the value of x when y is 9, we first need to understand direct variation. When two variables vary directly, their ratio remains constant. This means we can set up a proportion using the values we know.
From the information given, we know that:
- x = 12 when y = 3
Using this, we can write the equation:
x/y = k (where k is the constant of variation)
Substituting the known values:
12/3 = k
Thus, k = 4.
Now, to find the value of x when y = 9, we will use the constant k:
x/9 = 4
From this, we can solve for x:
x = 4 * 9
x = 36.
So, the value of x when y is 9 is 36.