Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
x
48
63
66
y
16
21
22
what is the constant of variation?
To determine if y varies directly with x, we need to check if the ratio of y to x is always the same. Let's calculate the ratio for each pair of values:
For x = 48, y = 16 --> y/x = 16/48 = 1/3
For x = 63, y = 21 --> y/x = 21/63 = 1/3
For x = 66, y = 22 --> y/x = 22/66 = 1/3
The ratio y/x is always equal to 1/3, which means that y varies directly with x.
The constant of variation is 1/3.
The function rule can be written as y = (1/3)x.