1. The problem states that a football team was on the 35 yard line and lost 12 yards on a play. 2. We need to find the integer that represents the new position after losing 12 yards. 3. The formula to find the new position is: $$\text{New position} = \text{Starting position} - \text{Yards lost}$$ 4. Substitute the values: $$\text{New position} = 35 - 12$$ 5. Perform the subtraction: $$35 - 12 = 23$$ 6. Therefore, the integer representing the result of this situation is $23$. This means the team is now on the 23 yard line after losing 12 yards.