Explanation:

- The word "slack" typically means loose or lacking tension, but it can also mean lacking attention to detail or care, which is more in line with being casual or negligent in attitude.

- Careless: This matches the reflection of being negligent or inattentive. Carelessness is a direct synonym for a 'slack' attitude, showing neglect or indifference in manners.

- Lively: Means vibrant or full of life, which is quite the opposite of 'slack.'

- Keen: Means eager or enthusiastic. Again, this doesn't match the meaning of 'slack.'

- Active: Refers to engaging in action or being energetic, which contrasts with the passive nature typically associated with 'slack.'

Thus, the most appropriate synonym for "slack" is Careless.