Prices from a brunch restaurant are shown below. Find the rate of change for the situation.

[You can use Slope Formula m, equals, start fraction, y, start subscript, 2, end subscript, minus, y, start subscript, 1, end subscript, divided by, x, start subscript, 2, end subscript, minus, x, start subscript, 1, end subscript, end fractionm=
x
2

−x
1


y
2

−y
1





OR add the table to Desmos and type y, start subscript, 1, end subscript, \sim, m, x, start subscript, 1, end subscript, plus, by
1

∼mx
1

+b to see mm ]

[Enter the number only]
Toppings Waffle Price
33 1616
22 1414
00 1010

1 answer

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:

  1. For 0 toppings, the price is 10: \((0, 10)\)
  2. For 22 toppings, the price is 14: \((22, 14)\)
  3. 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).