Question

Use the image to answer the question. Line graph titled 'Average Weight of a Dog' with age in months on the x-axis (ranging from 0 to 10) and average weight in pounds on the y-axis (ranging from 0 to 60). Black dots represent data points at each month: at 0 months (0 lbs), 1 month (5 lbs), 2 months (11 lbs), 3 months (16 lbs), 4 months (18 lbs), 6 months (24 lbs), 8 months (38 lbs), 9 months (42 lbs), and 10 months (49 lbs). An orange line of best fit shows a steady upward trend in weight as the dog ages. A veterinarian collected data on the average weight of dogs by age in months. Interpret the slope and the y 𝑦 -intercept (0,0) ( 0 , 0 ) of the linear model, using the ordered pair (9,42) ( 9 , 42 ) . Round the slope to the nearest hundredth. (1 point) Responses Every month, a dog averages a gain of 4.3 pounds and weighs 0 pounds at birth. Every month, a dog averages a gain of 4.3 pounds and weighs 0 pounds at birth. Every month, a dog averages a gain of 4.67 pounds Every month, a dog averages a gain of 4.67 pounds Every 4.67 months, a dog averages a gain of 1 pound and weighs 0 pounds at birth. Every 4.67 months, a dog averages a gain of 1 pound and weighs 0 pounds at birth. Every month, a dog averages a gain of 0.21 pounds and weighs 0 pounds at birth. Every month, a dog averages a gain of 0.21 pounds and weighs 0 pounds at birth.

Answer 1

To interpret the slope and the y-intercept of the linear model from the provided data points, we will first calculate the slope using the ordered pair (9, 42).

1. **Finding the Slope:**
The slope (m) of a line connecting two points (x1, y1) and (x2, y2) is given by the formula:
\[
m = \frac{y2 - y1}{x2 - x1}
\]
Taking the pair (0, 0) as the first point and (9, 42) as the second point:
- \(x1 = 0\), \(y1 = 0\)
- \(x2 = 9\), \(y2 = 42\)

Plugging in the values:
\[
m = \frac{42 - 0}{9 - 0} = \frac{42}{9} \approx 4.67
\]

2. **Interpretation of the Slope:**
The slope of approximately 4.67 means that every month, a dog averages a gain of about 4.67 pounds.

3. **Y-Intercept:**
The y-intercept of the line is the point where the line crosses the y-axis, which occurs when x = 0. From the data, (0, 0) indicates that when the dog is 0 months old (at birth), the average weight is 0 pounds.

### Conclusion:
- Every month, a dog averages a gain of 4.67 pounds and weighs 0 pounds at birth. Thus, the correct response based on the interpretation of the slope and the y-intercept is: **"Every month, a dog averages a gain of 4.67 pounds and weighs 0 pounds at birth."**