1. **State the problem:** We are given a table showing the baby's age $x$ in months and the corresponding average length $y$ in inches: | Age $x$ (months) | 0 | 1 | 2 | 3 | |------------------|---|---|---|---| | Length $y$ (inches) | 30 | 31 | 32 | 33 | We need to find the equation that best represents the relationship between $x$ and $y$. 2. **Analyze the data:** Observe how $y$ changes as $x$ increases. - When $x=0$, $y=30$ - When $x=1$, $y=31$ - When $x=2$, $y=32$ - When $x=3$, $y=33$ 3. **Find the pattern:** The length $y$ increases by 1 inch for every 1 month increase in age $x$. 4. **Formulate the equation:** Since $y$ starts at 30 when $x=0$ and increases by 1 for each increase in $x$, the equation is: $$y = 30 + x$$ 5. **Check the options:** - A: $y = 30x$ (would be 0 at $x=0$, 30 at $x=1$, which does not match) - B: $x = 30 + y$ (does not fit the data pattern) - C: $x = 30y$ (does not fit the data pattern) - D: $y = 30 + x$ (matches the pattern exactly) **Final answer:** The equation that best represents the relationship is $y = 30 + x$.