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We are given the equation \( y = 56 + 4x \), where:

- \( y \) represents the total length of the road in miles.
- \( x \) represents the number of days the crew has worked.

To answer the questions:

1. **What was the road's length when the crew started working?**
   When the crew started working, the number of days \( x = 0 \). Substituting \( x = 0 \) into the equation:
   \[
   y = 56 + 4(0) = 56
   \]
   So, the road's length at the start was **56 miles**.

2. **What is the change per day in the road's length?**
   The change in road length per day is given by the coefficient of \( x \) in the equation, which is **4 miles per day**. This means the road length increases by 4 miles each day.

Would you like more details on any of these calculations? Here are five follow-up questions for further exploration:

1. What would be the total length of the road after 10 days?
2. How would the equation change if the crew worked at a rate of 5 miles per day?
3. What would happen to the equation if the crew started with a road length of 60 miles instead?
4. How long would it take for the road to reach a total length of 100 miles?
5. How does changing the initial length of the road affect the overall equation?

**Tip:** When interpreting linear equations, the constant represents the starting value, and the coefficient of the variable represents the rate of change.

What was the road's length when the crew started working? What is the change per day in the road's length?

Explore how to determine the initial length and daily change in road length using the linear equation y = 56 + 4x. This problem involves basic algebra concepts suitable for Grades 6-8.

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