To interpret the slope and the y-intercept of the linear model, let's first establish what these terms mean in the context of the scenario given.
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Slope: The slope represents the change in weight of a dog for each additional month of age. In this case, it seems the slope is meant to indicate the average weight gain per month for dogs.
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Y-Intercept: The y-intercept represents the starting point when age (in months) is zero, which can be interpreted as the average weight of a newborn dog.
From the ordered pair (9, 42), we can conclude that at 9 months of age, the average weight of the dog is 42 pounds.
Now, if we assume that the slope has been calculated correctly (the problem suggests a slope of approximately 4.67), this means:
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Interpretation of Slope: Every month, a dog averages a gain of 4.67 pounds. This matches with the correct response option.
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Interpretation of Y-Intercept (0,0): While the provided options suggest weights at birth, it is generally accepted that this would mean a dog weighs 0 pounds at birth, although in reality this value would not be literally true for actual dogs but is often an estimation in these types of models.
Based on these interpretations, the most accurate response is:
Every month, a dog averages a gain of 4.67 pounds.