Question

Pizza General charges 10 dollars per medium pizza and a 5-dollar delivery fee.
What is the slope of line p? In other words, if you add 1 pizza to your order, how many dollars do you need to add to the total cost?
x
y
p
(1, 15)(2, 25)
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
=

Answer 1

To determine the slope of the line representing the total cost of the pizzas, we need to analyze the relationship between the number of pizzas (x-axis) and the total cost (y-axis).

Given:

- Each medium pizza costs $10.
- There is a $5 delivery fee.

The total cost \(y\) can be expressed as:

\[
y = 10x + 5
\]

where \(x\) is the number of pizzas ordered.

### Finding the slope:
The slope \(m\) of a linear equation in the form \(y = mx + b\) is the coefficient of \(x\). In this case:

- The slope \(m = 10\).

### Interpretation of the slope:
This means that for each additional pizza added to the order, the total cost increases by $10.

### Further verification using points:
Let's use the given points from your description:
- At \( (1, 15) \):
- Total cost for 1 pizza: \( 10(1) + 5 = 15 \) (Correct)

- At \( (2, 25) \):
- Total cost for 2 pizzas: \( 10(2) + 5 = 25 \) (Correct)

### To calculate using the definition of slope:
Using the formula for slope \( \text{slope} = \frac{\text{change in } y}{\text{change in } x} \):

1. Change in \( y \) from point (1, 15) to (2, 25):
- \( 25 - 15 = 10 \)

2. Change in \( x \):
- \( 2 - 1 = 1 \)

Now, using the slope formula:

\[
\text{slope} = \frac{10}{1} = 10
\]

### Conclusion:
The slope of the line \( p \) is:

\[
\text{Slope} = 10
\]

Thus, if you add 1 pizza to your order, you need to add **$10** to the total cost.