Question

1. adeline collected data to determine the association between age of an infant and its weight. she modeled the equation y = 1.25x + 7 for the line of best fit. the independent variable, x, is time in months and the dependent variable, y, is weight in pounds. what does the y-intercept mean in this context?

a the infant’s starting weight is 7 pounds.
b the infant’s starting weight is 1.25 pounds.
c the infant’s weight increases by an additional 7 pounds for each month.
d the infant’s weight increases by an additional 1.25 pounds for each month.

Explanation:

Step1: Recall linear equation form

The linear equation is \( y = mx + b \), where \( b \) is the y - intercept (when \( x = 0 \)).

Step2: Analyze the given equation

The equation is \( y=1.25x + 7 \). Here, \( x \) is age in months (independent variable) and \( y \) is weight (dependent variable). When \( x = 0 \) (age = 0 months, i.e., at birth), \( y=7 \). So the y - intercept (7) represents the infant's starting weight (at 0 months).

Step3: Evaluate the options

• Option A: Matches the interpretation of the y - intercept (starting weight at \( x = 0 \)).
• Option B: The coefficient of \( x \) is 1.25, not related to starting weight.
• Option C: The slope (1.25) represents the rate of weight increase per month, not the y - intercept.
• Option D: The slope is 1.25, not the y - intercept.

Answer:

A. The infant’s starting weight is 7 pounds