To create a linear equation that represents the situation, we can define \( y \) as the distance to your house in blocks and \( x \) as the time in minutes you have been walking.
Initially, the distance to your house is 41 blocks. With each passing minute, you walk 3 blocks closer to home. Therefore, after \( x \) minutes, the distance \( y \) to your house can be represented as follows:
\[ y = 41 - 3x \]
Here, 41 is the initial distance, and \( 3x \) represents the distance you have walked after \( x \) minutes.
Next, we set \( y = 0 \) to find out how many minutes it will take to reach home:
\[ 0 = 41 - 3x \]
Now, solve for \( x \):
\[ 3x = 41 \] \[ x = \frac{41}{3} \approx 13.67 \]
Rounding to the nearest minute, it will take approximately 14 minutes to get home.
Thus, the correct answer to the equation is:
Response: \( y = 41 - 3x \) and it will take approximately 14 minutes to get home.