To determine if the equation 5x = 3y represents a direct variation, we need to rewrite it in the standard form of a direct variation equation, which is y = kx, where k is the constant of variation.
Starting with the given equation, we can solve for y:
5x = 3y
Dividing both sides by 3 gives:
y = (5/3)x
Now, we can see that this is in the form of y = kx, where k is 5/3. Therefore, the equation does represent a direct variation, and the constant of variation is:
k = 5/3
This means that for every 1 unit increase in x, y will increase by (5/3) units, confirming that there is a direct relationship between x and y in this equation.