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.
Desmos Link
(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.
Desmos Link
(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.
Answers
GPT-4o mini
Let's break this down step by step:
1. **Your rate of change**: You are walking 3 blocks per minute towards your house, so your rate of change is -3 (since the distance to your house decreases).
2. **Your starting amount**: You start at 41 blocks away from home, so your starting amount is 41.
3. **Equation in slope-intercept form**: In this case, let \( y \) represent the distance to your house (in blocks) and \( x \) represent the time in minutes. The slope (rate of change) is -3 and the starting distance (y-intercept) is 41. The equation can be written in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Thus, the equation is:
\[
y = -3x + 41
\]
4. **Time to get home**: To determine how long it takes to walk 41 blocks at a speed of 3 blocks per minute, we can use the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{41 \text{ blocks}}{3 \text{ blocks/min}} \approx 13.67 \text{ minutes}
\]
Rounding to the nearest minute, it will take approximately 14 minutes to get home.
Putting everything together:
- Your rate of change in this situation is: **-3**
- Your starting amount is: **41**
- The equation that represents the situation in slope-intercept form is: **y = -3x + 41**
- It will take: **14 minutes** to get home.
1. **Your rate of change**: You are walking 3 blocks per minute towards your house, so your rate of change is -3 (since the distance to your house decreases).
2. **Your starting amount**: You start at 41 blocks away from home, so your starting amount is 41.
3. **Equation in slope-intercept form**: In this case, let \( y \) represent the distance to your house (in blocks) and \( x \) represent the time in minutes. The slope (rate of change) is -3 and the starting distance (y-intercept) is 41. The equation can be written in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Thus, the equation is:
\[
y = -3x + 41
\]
4. **Time to get home**: To determine how long it takes to walk 41 blocks at a speed of 3 blocks per minute, we can use the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{41 \text{ blocks}}{3 \text{ blocks/min}} \approx 13.67 \text{ minutes}
\]
Rounding to the nearest minute, it will take approximately 14 minutes to get home.
Putting everything together:
- Your rate of change in this situation is: **-3**
- Your starting amount is: **41**
- The equation that represents the situation in slope-intercept form is: **y = -3x + 41**
- It will take: **14 minutes** to get home.