https://file.aiquickdraw.com/mathbot/file/1729618162194zdgjvchh.jpg

To solve this problem, we need to determine the length of the pipe when its mass is 80 kg, given that the graph shows a linear relationship between mass and length.

### Step-by-step approach:

1. **Identify slope of the graph (mass per meter):**
   - From the graph, at 12 meters, the mass is 60 kg.
   - The slope (mass per unit length) can be calculated as:
     \[
     \text{slope} = \frac{\text{change in mass}}{\text{change in length}} = \frac{60 \, \text{kg}}{12 \, \text{m}} = 5 \, \text{kg/m}
     \]
   So, for every meter of pipe, the mass increases by 5 kg.

2. **Find the length for 80 kg:**
   - Using the slope, the mass \(M\) is directly proportional to the length \(L\), with the equation:
     \[
     M = 5 \times L
     \]
   - To find the length when the mass is 80 kg, solve for \(L\):
     \[
     80 = 5 \times L \quad \Rightarrow \quad L = \frac{80}{5} = 16 \, \text{m}
     \]
   
### Final Answer:
The length of the pipe with a mass of 80 kg is **16 meters**.

Would you like more details or have any further questions?

Here are 5 related questions to explore this concept further:
1. What would the length of the pipe be if the mass was 100 kg?
2. How would the graph look if the mass per meter doubled?
3. Can you find the mass of a 5-meter-long pipe using this relationship?
4. How would the equation change if the relationship between mass and length was not linear?
5. What would the mass be for a 20-meter section of this pipe?

**Tip:** Always look for proportional relationships when dealing with straight-line graphs!

The mass of a section of pipe depends on its length. If the graph continues in the same way, how long is a section of pipe with a mass of 80 kg?

Learn how to find the length of a section of pipe with a mass of 80 kg using linear relationships. The mass increases by 5 kg per meter of length, and the problem involves proportional reasoning and solving linear equations. Suitable for Grades 7-9.

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