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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.

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(4 points)
Your rate of change in this situation is (only answer with an integer)

Your starting amount is (Only answer with an integer)

The equation that represents the situation in slope intercept form is y=

It will take minutes (to the nearest minute), to get home.

1 answer

Let's break down the situation step by step:

  1. Rate of Change: You are walking towards your home, decreasing the distance. Since you walk 3 blocks per minute, the rate of change in distance is -3 blocks/minute (since you are getting closer to home).

    Rate of Change = -3

  2. Starting Amount: The starting distance from your home is 41 blocks.

    Starting Amount = 41

  3. Equation in Slope-Intercept Form: The slope-intercept form of a linear equation is given by:

    \[ y = mx + b \]

    where:

    • \(y\) is the distance from home,
    • \(m\) is the rate of change (-3),
    • \(x\) is the time in minutes,
    • \(b\) is the starting amount (41).

    Therefore, the equation becomes:

    \[ y = -3x + 41 \]

  4. Time to Get Home: To find the total time it will take to reach home, set \(y = 0\) (when you have arrived home) and solve for \(x\):

    \[ 0 = -3x + 41 \ 3x = 41 \ x = \frac{41}{3} \approx 13.67 \text{ minutes} \]

    Rounding to the nearest minute gives:

    It will take approximately 14 minutes to get home.

In summary:

  • Rate of Change: -3
  • Starting Amount: 41
  • Equation: \(y = -3x + 41\)
  • Time to get home: 14 minutes.