Final answer:
To find the constant of variation for the direct relationship between x and y, we use the known values y = 30 when x = 5 in the equation y = kx, which gives us k = 6 as the constant of variation.
Step-by-step explanation:
To solve for the constant of variation, we need to identify the known and the unknown values given in the question where y varies directly as x. According to the problem statement, when x is 5, y is 30. This allows us to set up the equation of direct variation which is y = kx, where k is the constant of variation.
1. Identify the known. y = 30.00 when x = 5.
2. Identify the unknown. We need to solve for k in the equation y = kx.
3. Express the answer as an equation. Start with the direct variation equation y = kx and substitute the given values.
We then have 30 = k(5), which we can solve by dividing both sides by 5 to isolate k. This gives us k = 30/5, which simplifies to k = 6.
Therefore, the constant of variation is 6.