Question

5. A water tank is being emptied and replaced with another one. Desmos Link (7 points) How much water did the tank have when it started being drained? This would represent the of the line graphed. The tank is empty after . This would be the of the line graphed. The tank is emptying at a rate of . This represents a(n) slope The equation that would represent this scenario would be

Answer 1

To solve this problem, we need to gather and clarify the given information regarding the water tank, specifically:

1. The initial amount of water in the tank when it started being drained.
2. The time it takes for the tank to become empty.
3. The rate at which the tank is emptying.

Assuming the information would be typically provided in a context (like a chart or graph) in Desmos, here's how we can structure the answer:

### Sample Breakdown (you will need to fill in actual numbers):

1. **Initial Amount of Water**: Let's say the tank initially had \( A \) liters of water. This would be represented as the **y-intercept** \( (0, A) \) on the graph, where \( A \) is the vertical value when time \( t = 0 \).

2. **Time to Empty the Tank**: Let’s say the tank takes \( T \) hours to be fully drained. This would be represented as the **x-intercept** \( (T, 0) \) on the graph, where the vertical value is 0, indicating the tank is empty.

3. **Rate of Emptying**: If the tank is emptying at a rate of \( R \) liters per hour, this represents the **slope** of the line graphed, which we would express as negative because the volume of water is decreasing. Thus the slope \( m \) would be \( -R \).

### Equation of the Line

The equation of the line representing this scenario in slope-intercept form \( y = mx + b \) can be derived using the following information:

- The y-intercept \( b = A \) (initial amount of water).
- The slope \( m = -R \) (negative since the tank is being drained).

Thus, the equation representing the scenario would be:

\[
y = -R \cdot t + A
\]

Where \( y \) is the amount of water in the tank at time \( t \).

### Example filled with hypothetical numbers:

1. Initial amount of water \( A = 100 \) liters.
2. The tank takes \( T = 5 \) hours to empty.
3. The tank is emptying at a rate of \( R = 20 \) liters/hour.

Thus, we get:

- Initial amount of water: 100 liters (y-intercept)
- Time to empty: 5 hours (x-intercept)
- Rate of emptying: 20 liters/hour (negative slope)

Resulting in the equation:

\[
y = -20t + 100
\]

This describes the amount of water in the tank over time as it drains.

Feel free to replace the hypothetical numbers with actual values from your context, and this format should help articulate the entire scenario clearly.