3. 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)

Question

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 representing the situation where you are walking home, we can define:

• \( x \) as the number of minutes you walk.
• \( y \) as the number of blocks remaining until you reach home.

Since you start with 41 blocks and walk at a rate of 3 blocks per minute, the number of blocks remaining after walking for \( x \) minutes can be expressed as:

\[ y = 41 - 3x \]

Linear equation:

So the linear equation is:

\[ y = 41 - 3x \]

How many minutes will it take to get home?

To find out how long it will take to get home, we want to determine when \( y = 0 \) (when you have 0 blocks left). Setting the equation to zero:

\[ 0 = 41 - 3x \]

Now, solve for \( x \):

1. Rearrange the equation: \[ 3x = 41 \]

2. Divide by 3: \[ x = \frac{41}{3} \approx 13.67 \]

Rounding to the nearest whole minute, it will take approximately 14 minutes to get home.