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).
1 answer