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

Answer 1

To create a linear equation that represents the distance to your house as you walk, we can start by defining the variables:

- Let \( y \) represent the distance (in blocks) to your house.
- Let \( x \) represent the time (in minutes) you have been walking.

Initially, when you haven't started walking yet, the distance to your house is 41 blocks, so when \( x = 0 \), \( y = 41 \).

As you walk, you decrease the distance to your house at a rate of 3 blocks per minute. Thus, for every minute you walk (every increase in \( x \)), your distance \( y \) decreases by 3 blocks.

The linear equation representing this situation can be set up as follows:

1. The slope (rate of change) is \(-3\) (since the distance decreases).
2. The y-intercept (starting distance when \( x = 0 \)) is 41.

Putting it all together, the linear equation is:

\[ y = 41 - 3x \]

So, in the form you provided, the linear equation is:

**Linear equation: \( y = 41 - 3x \)**