1. **State the problem:** Max fills a bathtub with water. After 5 minutes, there are 11 gallons, and after 10 minutes, there are 22 gallons. We need to find an equation relating gallons $g$ to time $t$ and determine if the relationship is linear. 2. **Identify the type of function:** Since the amount of water increases over time, we suspect a linear relationship of the form $$g = mt + b$$ where $m$ is the rate of change (gallons per minute) and $b$ is the initial amount of water. 3. **Calculate the rate of change $m$:** $$m = \frac{\text{change in gallons}}{\text{change in time}} = \frac{22 - 11}{10 - 5} = \frac{11}{5} = 2.2$$ gallons per minute. 4. **Find the initial amount $b$:** At $t=0$, the tub is empty (no water), so $b=0$. 5. **Write the equation:** $$g = 2.2t$$ 6. **Check if the function is linear:** The equation is in the form $$g = mt + b$$ with $m=2.2$ and $b=0$, which is a linear function. **Final answer:** $$g = 2.2t$$ The relationship represents a linear function because it is in the form $y = mx + b$ with $b=0$.