https://file.aiquickdraw.com/mathbot/file/17285942962783foo0k7u.jpg

Let's go through each part of the problem from the image.

### Given Scenario:
- A 900-gallon tank is initially full and is being drained at a rate of 30 gallons per minute.

### Part (a):
**Task**: Write a formula for a linear function \( W(t) \) that gives the number of gallons of water in the tank after \( t \) minutes.

The general form for a linear function is:
\[
W(t) = W_0 - Rt
\]
Where:
- \( W_0 \) is the initial amount of water (900 gallons),
- \( R \) is the rate at which the tank is being drained (30 gallons per minute),
- \( t \) is the time in minutes.

Thus, the function is:
\[
W(t) = 900 - 30t
\]

### Part (b):
**Task**: How much water is in the tank after 7 minutes?

Using the formula from (a):
\[
W(7) = 900 - 30(7) = 900 - 210 = 690
\]
After 7 minutes, the tank contains 690 gallons of water.

### Part (c):
**Task**: Graph the function \( W(t) \) and identify and interpret the intercepts.

1. **Intercepts**:
   - **Y-intercept**: This occurs when \( t = 0 \). The tank starts with 900 gallons, so the y-intercept is \( (0, 900) \).
   - **X-intercept**: Set \( W(t) = 0 \) to find when the tank is empty.
     \[
     0 = 900 - 30t \quad \Rightarrow \quad 30t = 900 \quad \Rightarrow \quad t = 30
     \]
     So, the x-intercept is \( (30, 0) \), meaning the tank is empty after 30 minutes.

2. **Graph**: 
   The correct graph for this function shows a line starting at \( (0, 900) \) and descending to \( (30, 0) \). Therefore, **Graph B** is correct.

Would you like more detailed steps or clarification on any part?

### Relative Questions:
1. How would the equation change if the initial water volume was different?
2. What if the draining rate was faster, say 50 gallons per minute—how would the graph shift?
3. Can you derive the slope of the line directly from the scenario without forming the equation?
4. What do the intercepts represent in real-life terms?
5. How can you check the graph without using graphing software?

### Tip:
When graphing linear equations, always check both intercepts to ensure the graph accurately reflects the situation.

A 900-gallon tank is initially full of water and is being drained at a rate of 30 gallons per minute. Complete parts (a) through (c) below.

Learn how to solve and graph the linear equation for a 900-gallon tank that is being drained at a rate of 30 gallons per minute. This problem covers key algebraic concepts, including linear equations, slope-intercept form, and graph interpretation. Suitable for students in Grades 8-10.

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