0,0. 1,5. 2,10. 3,16. 4,18. 6,24. 8,38. 10,50. A veterinarian collected data on the average weight of dogs by age in months. Interpret the slope and the y-intercept (0,0) of the linear model, using the ordered pair (42,9). Round the slope to the nearest hundredth.
The linear model can be represented by the equation y = mx + b, where y is the average weight of dogs and x is the age in months.
Using the points (0,0) and (42,9), we can calculate the slope (m) of the linear model:
m = (y2 - y1) / (x2 - x1)
= (9 - 0) / (42 - 0)
≈ 0.21
Rounding the slope to the nearest hundredth, the slope is 0.21.
The y-intercept (b) of the linear model is the value of y when x = 0. From the given data, we can see that the average weight of dogs at 0 months is 0. Therefore, the y-intercept is 0.
Interpreting the slope:
The slope of the linear model (0.21) indicates that for every 1 month increase in age, the average weight of dogs increases by approximately 0.21 pounds.
Interpreting the y-intercept:
The y-intercept (0) of the linear model indicates that at 0 months of age, the average weight of dogs is 0 pounds. However, it's important to note that this may not be a realistic value since dogs are typically born with some weight.
Overall, these interpretations give insights into the relationship between the age of dogs and their average weight based on the collected data.