To interpret the slope and the y-intercept of the linear model using the given ordered pair (9, 42) and considering the model's context of average weight of dogs by age in months, follow these steps:
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Slope Interpretation:
- The slope indicates how much weight the dog gains on average for each additional month of age.
- To find the slope, we note from the point (9, 42) that at 9 months, the dog weighs 42 pounds.
- If we assume a constant rate of gain, we would typically have another point to calculate the slope directly. However, if we consider this point and a hypothetical starting point at birth (0 months, 0 pounds), we can calculate the slope as: \[ \text{slope} = \frac{42 \text{ pounds} - 0 \text{ pounds}}{9 \text{ months} - 0 \text{ months}} = \frac{42}{9} \approx 4.67 \]
- This means, on average, a dog gains approximately 4.67 pounds each month.
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Y-intercept Interpretation:
- The y-intercept at (0,0) suggests that at the age of 0 months (birth), the average weight of the dog is 0 pounds.
Thus, rounding the slope to the nearest hundredth gives us 4.67.
Based on this interpretation, the correct response would be:
Every month, a dog averages a gain of 4.67 pounds.