To determine whether the equation 5x = 3y represents a direct variation, we first need to understand what direct variation means.
A direct variation exists when one variable is a constant multiple of another variable. The general form of a direct variation equation is y = kx, where k represents the constant of variation.
We can rewrite the original equation to isolate y:
- Start with 5x = 3y.
- To solve for y, divide both sides by 3:
- y = (5/3)x.
This equation is indeed in the form of y = kx, where k = 5/3. Therefore, we can conclude that the equation represents a direct variation.
So the constant of variation for the equation 5x = 3y is 5/3.