Question

the weight, in pounds, of a newborn baby t months after birth can be modeled by w. the table below has select values showing the linear relationship between t and w. determine the number of pounds the baby gains per month. t | w 5 | 12.25 7 | 14.75 9 | 17.25

Explanation:

Step1: Recall slope formula for linear relationship

The rate of change (pounds gained per month) in a linear relationship is given by the slope formula \( m=\frac{W_2 - W_1}{t_2 - t_1} \), where \( (t_1, W_1) \) and \( (t_2, W_2) \) are two points on the line.

Step2: Choose two points from the table

Let's take the first two points: \( (t_1, W_1)=(5, 12.25) \) and \( (t_2, W_2)=(7, 14.75) \).

Step3: Calculate the slope

Substitute into the slope formula: \( m=\frac{14.75 - 12.25}{7 - 5}=\frac{2.5}{2} = 1.25 \).
We can verify with another pair of points, say \( (7, 14.75) \) and \( (9, 17.25) \): \( m=\frac{17.25 - 14.75}{9 - 7}=\frac{2.5}{2}=1.25 \).

Answer:

The baby gains 1.25 pounds per month.