The slope of the equation \( y = 1.25x + 7 \) represents the rate of change of the dependent variable (weight) with respect to the independent variable (age in months). In this context, the slope is 1.25, which means that for each additional month (increase in \( x \)), the weight of the infant ( \( y \)) increases by 1.25 pounds.
Therefore, the correct interpretation of the slope in this context is: D. An infant's weight increases by an additional 1.25 pounds for each month.