To analyze the linear model based on the information provided, we need to interpret the slope and the y-intercept.
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Y-Intercept (0,0): This point indicates that when a dog is 0 months old (at birth), it weighs 0 pounds. In other words, at birth, the average weight of the dog is expected to be 0 pounds.
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Slope: The slope of the line represents the average weight gain of a dog per month. If we consider the ordered pair (9, 42) as a point on the line, we can interpret this as: at 9 months old, the average weight of the dog is 42 pounds.
To find the slope, we can use the general formula for the slope of a line:
\[ \text{slope} = \frac{\text{change in weight}}{\text{change in age}} \]
We need more points or data to understand how weight changes with age to calculate this slope accurately. However, if we round your given options, we could see that a slope of approximately 4.67 would suggest that every month a dog gains about 4.67 pounds.
Thus, based on the interpretation given, the response that fits best is:
Every month, a dog averages a gain of 4.3 pounds and weighs 0 pounds at birth.
However, if you are looking strictly for a rounded average based on the numerical value implied, the closest choice available for a monthly weight gain (especially as discussed with slope being stated as 4.67 originally) would yield that information. If the slope from other data indicated something specifically different, the corresponding option should align directly with that calculation.
Using the interpretations given, if the slope were indeed rounding to around 4.3, it would mean the dog is gaining about 4.3 pounds monthly. That's the essence of the model being conveyed depending on the representation made from the data.