Question

Question

Use the image to answer the question.

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 (9,42)
. Round the slope to the nearest hundredth.

(1 point)
Responses

Every 4.67 months, a dog averages a gain of 1 pound and weighs 0 pounds at birth.
Every 4.67 months, a dog averages a gain of 1 pound and weighs 0 pounds at birth.

Every month, a dog averages a gain of 0.21 pounds and weighs 0 pounds at birth.
Every month, a dog averages a gain of 0.21 pounds and weighs 0 pounds at birth.

Every month, a dog averages a gain of 4.67 pounds
Every month, a dog averages a gain of 4.67 pounds

Every month, a dog averages a gain of 4.3 pounds and weighs 0 pounds at birth.
Every month, a dog averages a gain of 4.3 pounds and weighs 0 pounds at birth.

Answer 1

To interpret the slope and the y-intercept based on the ordered pair (9, 42), we begin by identifying what the components represent in the context of the linear model.

1. Slope: The slope of a linear relationship shows how much the average weight of the dogs increases for each additional month of age. If we are given that the ordered pair (9, 42) indicates that at 9 months the weight is 42 pounds, we can determine that the slope is approximately \(0.21\) pounds per month. This means that, on average, a dog gains about 0.21 pounds each month.

2. Y-Intercept: The y-intercept occurs where the line crosses the y-axis, which is when age in months (x) is 0. In this context, the y-intercept indicates the average weight of the dog at birth. Given that the y-intercept is stated to be (0, 0), we interpret this to mean that a dog weighs approximately 0 pounds at birth.

Based on these interpretations, the correct response considering the slope of approximately 0.21 pounds per month and the birth weight of 0 pounds would be:

Every month, a dog averages a gain of 0.21 pounds and weighs 0 pounds at birth.