3x+6y=18 find the rate of change, initial value, and function rule and show what you did

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.