Question

What is the rate of change, and what does the rate of change mean in this context?
1
10
1
10
x
y
m
0
1
2
3
4
5
6
7
8
9
10
11
0
5
10
15
20
25
30
35
40
45
50
55
60
Number of pizzas
Total cost in dollars
Slope =
vertical distance
horizontal distance
= 10


The rate of change is
.

That means that for every
, you will
.

Answer 1

To find the rate of change in the context provided (which appears to relate the number of pizzas to the total cost), we can follow these steps:

1. **Understanding the slope formula**:
The rate of change (or slope, \( m \)) is calculated as the change in the dependent variable (total cost) divided by the change in the independent variable (number of pizzas).

\[
m = \frac{\Delta y}{\Delta x}
\]

In your case, it seems you have a change of \( \Delta y = 10 \) dollars and a corresponding change in \( \Delta x = 1 \) pizza.

2. **Calculating the rate of change**:
Since the provided data gives \( \Delta y = 10 \) (increase in cost) and \( \Delta x = 1 \) (increase in number of pizzas), we can compute:

\[
m = \frac{10}{1} = 10
\]

Thus, the rate of change is **10**.

3. **Interpreting the rate of change**:
The rate of change tells us how much the total cost increases for each additional pizza purchased.

Therefore, you can state:

"The rate of change is **10**."

"That means that for every **1 pizza**, you will **increase the total cost by $10**."

This means every time you buy one more pizza, the total cost goes up by $10.