An equation of the line of best fit shown in the scatter plot is [tex]y = 92x + 22[/tex].

Part A: What is the meaning of 92 in this model?

A. On average, children will be about 9 inches taller when they are 2 years old.
B. On average, children will grow about 9 inches every year in their first five years.
C. On average, children grow about 9 inches every 2 years in their first five years.
D. On average, children will grow 2 inches every year for their first 9 years.

Part B: What does 22 mean in this model?

A. The y-intercept, 22, means that on average, babies grow about 22 inches in the first five years.
B. The y-intercept, 22, means that on average, babies are 22 inches in length when born.
C. The y-intercept, 22, means that on average, two-year-olds are 22 inches tall.
D. The y-intercept, 22, means that on average, babies will grow about 22 inches in the first 2 years.

The '92' in the given equation is the slope, representing the average growth rate per year. The '22' is the y-intercept, representing the initial condition at birth, implying that on average, babies are about 22 inches in length when born.

Explanation:

In the given equation, y=92x+22, '92' and '22' hold specific meanings with respect to the context of the question. '92', being the coefficient of 'x', represents the slope of the line. This means on average, for every unit increase in 'x' (which could be years, or some other measurement of time), 'y' (which could represent height, or some other measure of growth) will increase by 92 units. Therefore, it signifies the average growth rate per year.

The '22' in the model signifies the y-intercept on the scatter plot which happens when 'x' is at zero. In this context, it could represent the initial condition at birth (I.e., average length or height of a newborn baby). Here, it implies that on average, babies are about 22 inches in length when born.

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