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 given linear model represents the relationship between the age of a dog in months (x) and its average weight (y). The ordered pair (42,9) means that at 42 months, the average weight of a dog is 9 pounds.
The slope of the linear model represents the rate of change in the average weight of dogs per month. To find the slope, we need to determine how much the average weight changes when the age increases by 1 month.
Let's use the information given to calculate the slope of the linear model:
slope = (change in y) / (change in x)
Using the ordered pair (42,9), we can calculate the change in y and change in x as follows:
change in y = 9 - 0 = 9
change in x = 42 - 0 = 42
slope = (9) / (42) = 0.21 (rounded to the nearest hundredth)
Therefore, the slope of the linear model is approximately 0.21. This means that on average, the weight of dogs increases by about 0.21 pounds for each additional month of age.
The y-intercept of the linear model (0,0) represents the estimated weight of a dog at 0 months of age (at birth). In this case, it suggests that a newborn dog has an estimated weight of 0 pounds. However, it is important to note that this might not be a realistic interpretation, as dogs are not typically born without any weight.
In summary, the slope of the linear model (0.21) indicates the average increase in weight for each additional month of age, and the y-intercept (0,0) represents the estimated weight of a dog at birth.