1. **State the problem:** We need to write a function that models the height of Emily's rosemary bush over time. 2. **Identify the variables:** Let $x$ represent the number of years since planting, and $y$ represent the height of the rosemary bush in centimeters. 3. **Understand the growth pattern:** The bush starts at 5 cm and grows 3 cm each year. This is a linear growth, so the function will be of the form $$y = mx + b$$ where $m$ is the growth rate and $b$ is the initial height. 4. **Assign values:** Here, $m = 3$ (growth rate in cm/year) and $b = 5$ (initial height in cm). 5. **Write the function:** $$y = 3x + 5$$ 6. **Interpretation:** For any number of years $x$, multiply by 3 and add 5 to find the height $y$ of the rosemary bush. **Final answer:** $$y = 3x + 5$$