Final answer:
When y varies directly as x and y=16 when x=8, the constant of variation k is 2. Therefore, when x=16, y equals 2 times 16, which means y=32.
Step-by-step explanation:
If y varies directly as x, and y=16 when x=8, we can find the value of y when x=16 by setting up a proportion. In a direct variation, the ratio between y and x is constant. This means we can write the equation y = kx, where k is the constant of variation. To find k, we use the given values:
y = kx
16 = k × 8
k = 2
Once we have determined the constant of variation (k=2), we can use this to find y when x=16:
y = kx
y = 2 × 16
y = 32
So, when x is 16, y is 32, as y is directly proportional to x.