2. A boy is 29 inches tall when he is 1 year old and 66 inches tall when he is 15 years old. What is the rate of change? (Hint: time is always \( x \) )

To find the **rate of change** of the boy's height with respect to time, we'll use the concept of **slope** from linear functions. The rate of change represents how much the boy's height increases (or decreases) per year. ### Given: - **Point 1:** When \( x = 1 \) year, height \( y = 29 \) inches. - **Point 2:** When \( x = 15 \) years, height \( y = 66 \) inches. ### Formula for Rate of Change (Slope): \[ \text{Rate of Change} = \frac{\text{Change in Height}}{\text{Change in Time}} = \frac{y_2 - y_1}{x_2 - x_1} \] ### Plugging in the Values: \[ \text{Rate of Change} = \frac{66\, \text{inches} - 29\, \text{inches}}{15\, \text{years} - 1\, \text{year}} = \frac{37\, \text{inches}}{14\, \text{years}} \] ### Simplifying: \[ \text{Rate of Change} = \frac{37}{14} \approx 2.64\, \text{inches per year} \] ### Interpretation: The boy's height increases by approximately **2.64 inches each year**. ### Final Answer: The rate of change is 37⁄14 inches per year, that is, 37/14 in/year.