Final answer:
To find the value of p when q=6 in a direct variation equation, we use the given values p=63 when q=9. We find the constant of variation and substitute it into the equation to find p when q=6.
Step-by-step explanation:
To find the value of p when q=6 in the direct variation equation p varies directly with q, we can use the given information that p=63 when q=9.
From the direct variation equation, we know that p/q=k, where k is the constant of variation.
Using the given values, we can set up the equation 63/9=k to find the value of k. Solving for k, we get k=7.
Now, we can use the equation p/q=k to find the value of p when q=6, substituting q=6 and k=7 into the equation. Solving for p, we get p=6k=6*7=42.