To answer the questions, we need to calculate the slopes for each situation provided.
a. Slope for the bales of hay and mules
To find the slope, we use the formula:
\[ \text{slope} = \frac{\text{change in y}}{\text{change in x}} \]
Here, the number of bales of hay (y) corresponds to the number of mules (x):
- Points:
- (2 mules, 1 bale)
- (4 mules, 2 bales)
- (6 mules, 3 bales)
- (8 mules, 4 bales)
- (10 mules, 5 bales)
We can select any two points to calculate the slope. Let's use the first and last points:
\[ \text{slope} = \frac{5 - 1}{10 - 2} = \frac{4}{8} = \frac{1}{2} \]
Response area: The slope for the bales of hay and mules is 1/2.
b. Slope for cost and square footage of carpet
Using the same slope formula, we will look at the provided graph pin points.
- Points (cost in dollars, square footage):
- (10, 15)
- (20, 30)
- (30, 45)
- (40, 60)
- (50, 75)
We can again select any two points. Let's use the first and last points:
\[ \text{slope} = \frac{75 - 15}{50 - 10} = \frac{60}{40} = \frac{3}{2} \]
Response area: The slope for cost and square footage of carpet is 3/2.
c. Which situation has the greatest rate of change?
To compare the two slopes we've calculated:
- Slope for bales of hay and mules: 1/2
- Slope for cost and square footage of carpet: 3/2
Since 3/2 (1.5) is greater than 1/2 (0.5), the situation with the greatest rate of change is:
Response area: The situation with the greatest rate of change is the cost and square footage of carpet.
1 answer