Final answer:
The given equation 3y = 4x represents a direct variation with a constant of variation k = 4/3.
Step-by-step explanation:
Given equation: 3y = 4x
To determine if the equation represents a direct variation, we need to check if the ratio of y to x remains constant. In a direct variation, the ratio should be the same for all values of x and y.
To find the constant of variation, we can rewrite the equation in the form y = kx, where k is the constant of variation.
Dividing both sides of the equation by 3, we get: y = (4/3)x
Comparing this equation with y = kx, we can see that the constant of variation is k = 4/3.