Question

Use the figures below to help answer the questions.
# of Mules | Bales of Hay
2 | 1
4 | 2
6 | 3
8 | 4
10 | 5
square feet of carpet
(50, 75), (40, 60), (30, 45), (20, 30), (10, 15)
a. The slope for the bales of hay and mules is ____________
b. The slope for cost and square footage of carpet is ___________
c. Which situation has the greatest rate of change? ___________
Options: cos t/sq ft, 15, 2, hay/mule, 2, 1/2, 30, 5, 2/3, 3/2, 10

Answer 1

To determine the slopes for the scenarios given, we can define slope as the change in the dependent variable divided by the change in the independent variable.

### Part a: The slope for the bales of hay and mules
Based on the data given for mules and bales of hay:

- When the number of mules increases from 2 to 4 (an increase of 2 mules), the bales of hay increase from 1 to 2 (an increase of 1 bale).

Using the formula for slope:
\[
\text{slope} = \frac{\text{change in bales}}{\text{change in mules}} = \frac{2 - 1}{4 - 2} = \frac{1}{2}
\]

The slope for the bales of hay and mules is **1/2**.

### Part b: The slope for cost and square footage of carpet
Using the coordinates given (assuming the first value is square footage and the second value is cost):

- Let's calculate the slope between two points, for instance (50, 75) and (40, 60):
\[
\text{slope} = \frac{60 - 75}{40 - 50} = \frac{-15}{-10} = \frac{15}{10} = \frac{3}{2}
\]

The slope for cost and square footage of carpet is **3/2**.

### Part c: Which situation has the greatest rate of change?
Now, we compare the calculated slopes:
- Bales of hay per mule: **1/2** or **0.5**
- Cost per square foot of carpet: **3/2** or **1.5**

The greatest rate of change corresponds to **3/2**.

### Summary:
a. The slope for the bales of hay and mules is **1/2**.
b. The slope for cost and square footage of carpet is **3/2**.
c. Which situation has the greatest rate of change? **Cost per square footage of carpet** (3/2).