Final answer:
A direct variation equation relates two variables that are directly proportional to each other. In this case, the equation is y = (1/2)x.
Step-by-step explanation:
When two variables are directly proportional, it means that a change in one variable will result in a proportional change in the other variable. We can represent this relationship with a direct variation equation of the form y = kx, where k is the constant of variation.
In this case, we are given that y varies directly with x, and we have a specific data point: when x = 16, y = 8. We can use this information to find the constant of variation.
To find the constant of variation, we can substitute the values for x and y into the direct variation equation: 8 = k(16). We can then solve for k by dividing both sides of the equation by 16: k = 8/16 = 1/2.
Therefore, the direct variation equation that relates x and y in this problem is y = (1/2)x.