1. **State the problem:** We need to write an equation for the height $H$ of a plant in terms of time $t$ months after Scarlett bought it. 2. **Identify given information:** The plant grows 2.5 inches per month, and after 4 months, the plant is 22 inches tall. 3. **Understand the linear growth model:** The height $H$ changes linearly with time $t$, so the equation has the form $$H = mt + b$$ where $m$ is the growth rate (slope) and $b$ is the initial height (intercept). 4. **Calculate the growth rate $m$:** The problem states the plant grows 2.5 inches per month, so $$m = 2.5$$. 5. **Find the initial height $b$:** We know at $t=4$, $H=22$. Substitute into the equation: $$22 = 2.5 \times 4 + b$$ $$22 = 10 + b$$ $$b = 22 - 10 = 12$$ 6. **Write the final equation:** $$H = 2.5t + 12$$ **Note:** The answer given in the question, $H = \frac{2.5}{4}t + 22$, is incorrect because it treats 22 as the initial height and divides the growth rate by 4, which is not consistent with the problem statement. **Final answer:** $$H = 2.5t + 12$$