Final answer:
The direct variation between x and y is described by y = kx. By finding the constant of variation k when y is 2 and x is 3, we can then find y when x is 12, which is y = 8.
Step-by-step explanation:
If x and y vary directly, this means we can describe their relationship with a formula y = kx, where k is the constant of variation. Knowing that y is 2 when x is 3 gives us enough information to determine the constant of variation, k. We find k using the equation 2 = k(3), resulting in k being ⅓.
Once we have identified k, we can determine yy for when x is 12 using the direct variation formula. We substitute x with 12 in the equation y = ⅓(12) to find the new value of y.
Therefore, when x is 12, y will be 8.