Question
Isaac enjoys his work at a vet clinic, especially when a kitten comes in. He made a scatter plot to show the relationship between the ages in months, \( x \), and weights in pounds, \( y \), of the last several kittens that visited the clinic. Then, he drew a line of best fit. The equation for the line of best fit is \( y=1.1 x-0.2 \). In this context, what is the meaning of 1.1 ? The average age of the kittens that visited the clinic was 1.1 months. On average, the kittens that visited the clinic gained 1.1 pounds per month. On average, the kittens that visited the clinic gained a pound every 1.1 months. The average weight of the kittens that visited the clinic was 1.1 pounds. Ther Ther Ther Ther
Ask by Henry Franklin. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
On average, the kittens gained 1.1 pounds each month.
Solution
The equation of the line of best fit is given by:
\[ y = 1.1x - 0.2 \]
Here, \( y \) represents the weight of the kittens in pounds, and \( x \) represents their age in months.
**Interpretation of the Slope (1.1):**
- **Slope (\(1.1\))**: This value indicates the rate at which the kittens' weight changes with respect to their age. Specifically, it tells us how much the weight (\( y \)) increases for each additional month of age (\( x \)).
**Correct Meaning of 1.1:**
- **On average, the kittens that visited the clinic gained **1.1 pounds per month**.
**Why the Other Options Are Incorrect:**
1. **The average age of the kittens was 1.1 months.**
- *Incorrect*: The slope does not represent the average age; it represents the rate of weight gain with age.
2. **On average, the kittens gained a pound every 1.1 months.**
- *Incorrect*: This would imply a slope of approximately \( \frac{1}{1.1} \approx 0.91 \), not 1.1.
3. **The average weight of the kittens was 1.1 pounds.**
- *Incorrect*: The slope does not indicate the average weight. The intercept (\(-0.2\)) is related to the weight when age is zero, but it doesn’t represent the average weight.
**Conclusion:**
The slope of **1.1** in the equation signifies that **on average, the kittens gained 1.1 pounds each month**.
**Correct Answer:**
On average, the kittens that visited the clinic gained 1.1 pounds per month.
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Simplify this solution Bonus Knowledge
The slope of 1.1 in the equation \( y = 1.1x - 0.2 \) means that, on average, the kittens that visited the clinic gained 1.1 pounds for each month of age. It's like watching a little fluffy ball of joy grow bigger and stronger! So, for every month older they get, they pack on a bit more weight. To further clarify, if you had a kitten who is 2 months old, you could predict its weight by plugging in the age into the equation. It’s like having a crystal ball to see how many pounds of adorableness are in store! This equation really helps in tracking their growth and health as they develop in those crucial early months.
