The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.

To determine if the function rule you provided, \( y = 37 - 2x \), accurately models the relationship between the number of meals dispensed and the amount of pet food remaining, we'll analyze the given data points:

1. The data includes:
   • For \( x = 2 \) meals, \( y = 33 \) cups
   • For \( x = 5 \) meals, \( y = 27 \) cups
   • For \( x = 11 \) meals, \( y = 15 \) cups

Step 1: Check if \( y = 37 - 2x \) fits the data

Now, let's plug in the values of \( x \) into your proposed equation \( y = 37 - 2x \) and see if it produces the correct \( y \) values.

1. For \( x = 2 \): \[ y = 37 - 2(2) = 37 - 4 = 33 \] (This matches.)

2. For \( x = 5 \): \[ y = 37 - 2(5) = 37 - 10 = 27 \] (This matches.)

3. For \( x = 11 \): \[ y = 37 - 2(11) = 37 - 22 = 15 \] (This matches.)

Conclusion

Since all the calculations correspond to the given data points, the function rule you provided, \( y = 37 - 2x \), correctly models the situation described in the table. Thus, you are correct!