Question

1. an equation of the line of best fit shown in the scatter plot below is $y = \frac{9}{2}x + 22$. \

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(scatter plot titled children’s heights with x - axis age (yr) and y - axis height (in), data points plotted) \
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what is the meaning of $\frac{9}{2}$ in this model? \
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(handwritten answer: on average children grow about 9 inches every 2 years in their first 5 years) \
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what does 22 mean in this model? \
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(handwritten answer: the y - intercept. 22 means that on average, babies are 22 inches in length when born)

Explanation:

1. In the linear model \( y = \frac{9}{3}x + 22 \) (simplified to \( y = 3x + 22 \)), the coefficient of \( x \) (age in years) represents the rate of change of height with respect to age. Thus, 3 means height increases by 3 inches per year on average.
2. The constant term 22 is the y-intercept, which corresponds to the predicted height when age \( x = 0 \) (birth), so it is the average birth length.

Answer:

1. On average, a child's height increases by 3 inches per year.
2. The predicted height of a child at 0 years old (birth) is 22 inches.