Subjects algebra

Water Filling 1B0185

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1. **Problem Statement:** We are given a graph showing the relationship between the amount of water $W$ (in liters) in a fish tank and the time $T$ (in minutes) since the tank started being filled. The graph is a straight line starting at the origin $(0,0)$ and rising linearly to approximately $(9,90)$. 2. **Goal:** Write an equation that describes this proportional relationship between $W$ and $T$. 3. **Formula and Explanation:** Since the graph is a straight line through the origin, the relationship is proportional and can be written as: $$W = kT$$ where $k$ is the constant of proportionality (rate of filling in liters per minute). 4. **Find the constant $k$:** Using the point $(9,90)$ from the graph: $$k = \frac{W}{T} = \frac{90}{9} = 10$$ 5. **Write the equation:** $$W = 10T$$ 6. **Interpretation:** This means the tank is being filled at a rate of 10 liters per minute. 7. **Summary:** The equation describing the amount of water in the tank at time $T$ minutes is: $$W = 10T$$ This linear equation matches the graph and shows a proportional relationship between $W$ and $T$.