Your house is 41 blocks away and you walk 3 blocks per minute you are decreasing the distance as you walk home

Question

What is your rate of change without integer
Your starting amount is with integer
The equation that represents the situation in the slope intercept form is y =
It will take ___ minutes to get home

Answer 1

Let's analyze the situation step by step.

1. Starting Distance and Rate of Change:

   • The starting distance from home is 41 blocks.
   • You walk at a rate of 3 blocks per minute.
   • As you walk toward home, the distance to home decreases. Thus, your rate of change of distance can be represented as -3 blocks/minute (the negative sign indicates that the distance is decreasing).

2. Equation in Slope-Intercept Form:
   To write an equation in slope-intercept form \(y = mx + b\):

• Let \(y\) represent the distance to home.
• Let \(x\) represent the time in minutes.
• The slope (rate of change) \(m\) is -3 (since the distance decreases as time progresses).
• The y-intercept \(b\) is 41 (the initial distance from home at time \(x = 0\)).

So the equation is:
\[ y = -3x + 41 \]

3. Time to Get Home:
   To find out when you will reach home, set \(y = 0\) (meaning the distance to home is 0):

\[ 0 = -3x + 41 \]

Now, solving for \(x\): \[ 3x = 41 \]
\[ x = \frac{41}{3} \]
\[ x \approx 13.67 \text{ minutes} \]

Therefore, to summarize:

• The rate of change is -3 blocks per minute.
• The equation that represents the situation is \(y = -3x + 41\).
• It will take approximately 13.67 minutes to get home.