Question

You are traveling home from work. You are decreasing the distance as you walk home. Your house is 41 blocks away, and you walk 3 blocks per minute. Create a linear equation that represents the situation. (3 points) Linear equation: y= − x How many minutes will it take, to the nearest minute, to get home? minutes (round to the nearest whole minute)

Answer 1

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.