The usual interpretation of "rate of change" in this situation is "slope," which equals m = rise (change in y) over run (change in x).
Solve 3x + 6y = 18 for y: Dividing each term by 6 results in:
y = (-1/2)x + 3
The "rate of change" is the slope, m, which in turn is -1/2.
The function rule is y = f(x) = (-1/2)x + 3.
The initial value is the value of this function when x = 0 and is y(0) = 3.
