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To model this situation, we can let \( A \) represent the area of the house. According to the information given:
1. The area of the front yard is 4,200 ft².
2. The total area of the house plus the yard is equal to 8 times the area of the house alone.
We can express the total area as the sum of the area of the house and the area of the yard:
\[
\text{Total Area} = A + 4200
\]
According to the problem, this total area is also equal to 8 times the area of the house, which gives us the equation:
\[
A + 4200 = 8A
\]
This is the equation that models the real-world situation.