Answer:

Explanation:
The A-line in the unified classification system table is used to determine the plasticity index (IP) of a soil sample based on its liquid limit (WL). The equation for the A-line is given as IP = 0.73(WL - 20). Let's break down the equation and understand it further.

Understanding the Equation:
- IP: Plasticity index of the soil sample
- WL: Liquid limit of the soil sample

The equation states that the plasticity index (IP) is equal to 0.73 times the difference between the liquid limit (WL) and 20.

Explanation of the Equation:
- The value of 20 in the equation represents the reference liquid limit value below which the soil is considered to be non-plastic, meaning it does not exhibit plastic behavior.
- When the liquid limit (WL) is equal to or greater than 20, the difference between WL and 20 becomes positive, and multiplying it by 0.73 gives a positive value for the plasticity index (IP).
- As the liquid limit increases above 20, the plasticity index also increases. This indicates that the soil becomes more plastic and exhibits greater plastic behavior.
- On the other hand, if the liquid limit is less than 20, the difference between WL and 20 becomes negative, and multiplying it by 0.73 gives a negative value for the plasticity index (IP).
- A negative plasticity index is not physically meaningful, as it implies that the soil has a plasticity index less than zero, which is not possible.

Conclusion:
Therefore, the equation IP = 0.73(WL - 20) is used to calculate the plasticity index of a soil sample based on its liquid limit. The equation takes into account the reference liquid limit value of 20, which represents the threshold for plastic behavior in soils.