To create a linear equation that represents the situation, we can define the variables as follows:
- Let \( y \) be the distance to your house in blocks.
- Let \( x \) be the time in minutes.
Since you start 41 blocks away from home, we can express the distance \( y \) as:
\[ y = 41 - 3x \]
In this equation, the \( 3x \) term represents the distance you walk in blocks (3 blocks per minute) for \( x \) minutes. So, each minute you decrease the distance to your house by 3 blocks.
Now, we need to determine how many minutes it will take to get home. You will arrive home when \( y = 0 \):
\[ 0 = 41 - 3x \]
To solve for \( x \), we can rearrange the equation:
\[ 3x = 41 \]
\[ x = \frac{41}{3} \]
Calculating that gives:
\[ x \approx 13.67 \]
Rounded to the nearest whole minute, it will take approximately 14 minutes to get home.
So, your final answers are:
Linear equation: \( y = 41 - 3x \)
Minutes to get home: 14 minutes.