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Let's break down the problem.

The barrel contains 60 gallons of water initially, and it leaks 1 gallon every 10 minutes.

1. **Equation Setup**:
   We need to find the linear equation that represents the relationship between the gallons of water remaining in the barrel \( y \) and the number of minutes elapsed \( x \).

   - Initial water: 60 gallons (This is the **y-intercept**, \( b = 60 \)).
   - Rate of leakage: 1 gallon per 10 minutes. This is the **slope**, \( m \), but written as \( m = -\frac{1}{10} \), since the water is decreasing over time.

   Thus, the equation is:
   \[
   y = -\frac{1}{10}x + 60
   \]

2. **Graphing**:
   - The line starts at \( y = 60 \) when \( x = 0 \) (the initial point, \( (0, 60) \)).
   - For every 10 minutes, the water decreases by 1 gallon. So, at \( x = 100 \) minutes, the remaining water \( y \) would be \( 50 \) gallons.
   - This continues until the water is completely drained, i.e., \( y = 0 \). Setting \( y = 0 \) and solving for \( x \):
     \[
     0 = -\frac{1}{10}x + 60
     \]
     \[
     \frac{1}{10}x = 60 \quad \Rightarrow \quad x = 600
     \]
   Thus, the water runs out after 600 minutes.

3. **Plotting Points**:
   You can plot the points:
   - \( (0, 60) \)
   - \( (100, 50) \)
   - \( (200, 40) \)
   - \( (600, 0) \)

Would you like help with graphing this on your tool?

### 5 Related Questions:
1. What does the slope of the line represent in the context of this problem?
2. How would the graph change if the leakage rate doubled to 2 gallons every 10 minutes?
3. What is the significance of the y-intercept in real-world problems like this one?
4. If Jim refills the barrel halfway through, how would that affect the graph?
5. What would happen to the equation if the initial amount of water was different?

**Tip**: Always pay attention to the units (e.g., minutes vs. gallons), especially when defining the slope of a line.

A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Create and graph the equation for the gallons of water remaining in the barrel in terms of the number of minutes elapsed.

Learn how to solve and graph the linear equation representing the water leakage from a barrel. The problem involves determining the gallons of water remaining as time progresses, with a rate of 1 gallon per 10 minutes. This exercise covers linear equations, the slope-intercept form, and graphing. Suitable for students in Grades 7-9.

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