To find the rate of change (slope) for the prices of waffles based on the number of toppings, we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where:
- \(x\) represents the number of toppings
- \(y\) represents the waffle price
From the data provided:
- For 0 toppings, the price is 10: \((0, 10)\)
- For 22 toppings, the price is 14: \((22, 14)\)
- For 33 toppings, the price is 16: \((33, 16)\)
Let's look at the change between 0 and 22 toppings:
- \(x_1 = 0\), \(y_1 = 10\)
- \(x_2 = 22\), \(y_2 = 14\)
Calculating the slope:
\[ m = \frac{14 - 10}{22 - 0} = \frac{4}{22} = \frac{2}{11} \]
Next, let's compute the change from 22 to 33 toppings:
- \(x_1 = 22\), \(y_1 = 14\)
- \(x_2 = 33\), \(y_2 = 16\)
Calculating the slope:
\[ m = \frac{16 - 14}{33 - 22} = \frac{2}{11} \]
Now we can check the change between 0 and 33 toppings:
- \(x_1 = 0\), \(y_1 = 10\)
- \(x_2 = 33\), \(y_2 = 16\)
Calculating the slope:
\[ m = \frac{16 - 10}{33 - 0} = \frac{6}{33} = \frac{2}{11} \]
In each case, the rate of change (slope) is consistent.
Therefore, the answer is
\[ \frac{2}{11} \quad \text{(as a numeric answer, you should enter "0.181818")} \]
So, you can enter:
0.18 (rounding to two decimal places).