To interpret the slope and the y-intercept of the linear model representing the average weight of dogs by age:
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Y-Intercept (0,0): This indicates that when a dog is 0 months old (at birth), the average weight is 0 pounds. This point signifies that at birth, a dog has not gained any weight yet.
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Slope: The ordered pair (9, 42) indicates that at 9 months, the average weight of a dog is 42 pounds. To find the slope in terms of pounds per month, we need to understand how much weight increases as time goes on.
If we assume that the weight is linearly related to age in months, we can set up an equation based on a known slope (rise over run):
Slope \( m \) = \( \frac{\text{change in weight}}{\text{change in age}} = \frac{42 \text{ pounds} - 0 \text{ pounds}}{9 \text{ months} - 0 \text{ months}} = \frac{42}{9} \).
Calculating that gives us:
\( m \approx 4.67 \) pounds per month.
Now, rounding to the nearest hundredth, the slope is approximately 4.67.
- Final Interpretation:
Based on the slope and y-intercept, we can interpret the results as follows:
- The slope indicates that every month, a dog averages a gain of 4.67 pounds.
- The y-intercept indicates that a dog weighs approximately 0 pounds at birth.
Among the options provided, the correct interpretation would be:
- "Every month, a dog averages a gain of 4.67 pounds and weighs 0 pounds at birth."