Question
Which scenario best describes the graph: (1 point) Responses Juan starts with $30 in savings and increases his savings amount by $5 each week. Juan starts with $30 in savings and increases his savings amount by $5 each week. Juan starts with $30 in savings and increases his savings amount by $1 each week. Juan starts with $30 in savings and increases his savings amount by $1 each week. Juan starts with $5 in savings and increases his savings amount by $30 each week. Juan starts with $5 in savings and increases his savings amount by $30 each week. Juan saves $30 per week.
Y intercept is 30$ he start with it
Y intercept is 30$ he start with it
Answers
Answer
y axis goes up by 10 multiples until it reach 90
x axis goes up by time in weeks. in 4 weeks he has 50$
x axis goes up by time in weeks. in 4 weeks he has 50$
Answered by
GPT-4o mini
To determine which scenario best describes the graph with a y-intercept of $30, we need to analyze the different scenarios provided based on the initial amount of savings and how much the savings increase each week.
1. **Juan starts with $30 in savings and increases his savings amount by $5 each week.**
- Initial savings: $30
- Weekly increase: $5
- Equation: \( y = 30 + 5x \)
2. **Juan starts with $30 in savings and increases his savings amount by $1 each week.**
- Initial savings: $30
- Weekly increase: $1
- Equation: \( y = 30 + 1x \)
3. **Juan starts with $5 in savings and increases his savings amount by $30 each week.**
- Initial savings: $5
- Weekly increase: $30
- Equation: \( y = 5 + 30x \)
4. **Juan starts with $5 in savings and increases his savings amount by $30 each week.**
- Initial savings: $5
- Weekly increase: $30
- Equation: \( y = 5 + 30x \)
5. **Juan saves $30 per week.**
- Assuming he starts with $0, the equation would be \( y = 30x \).
From the scenarios, the first two have a y-intercept of $30, meaning both begin from $30 in savings. The crucial difference is their week-to-week increase, which affects the slope of the line in the graph.
However, since the question states that the y-intercept is $30 and doesn't specify the weekly increase as a factor in determining the correct graph, either of the first two scenarios can accurately represent the graph with a $30 starting amount.
***In conclusion, either of the first two scenarios is correct regarding the y-intercept of $30:***
- Juan starts with $30 in savings and increases his savings amount by $5 each week.
- Juan starts with $30 in savings and increases his savings amount by $1 each week.
If you need to choose just one scenario with a stronger emphasis on savings being incremented regularly, the first option might be the most intuitive as it suggests a higher increase over time.
1. **Juan starts with $30 in savings and increases his savings amount by $5 each week.**
- Initial savings: $30
- Weekly increase: $5
- Equation: \( y = 30 + 5x \)
2. **Juan starts with $30 in savings and increases his savings amount by $1 each week.**
- Initial savings: $30
- Weekly increase: $1
- Equation: \( y = 30 + 1x \)
3. **Juan starts with $5 in savings and increases his savings amount by $30 each week.**
- Initial savings: $5
- Weekly increase: $30
- Equation: \( y = 5 + 30x \)
4. **Juan starts with $5 in savings and increases his savings amount by $30 each week.**
- Initial savings: $5
- Weekly increase: $30
- Equation: \( y = 5 + 30x \)
5. **Juan saves $30 per week.**
- Assuming he starts with $0, the equation would be \( y = 30x \).
From the scenarios, the first two have a y-intercept of $30, meaning both begin from $30 in savings. The crucial difference is their week-to-week increase, which affects the slope of the line in the graph.
However, since the question states that the y-intercept is $30 and doesn't specify the weekly increase as a factor in determining the correct graph, either of the first two scenarios can accurately represent the graph with a $30 starting amount.
***In conclusion, either of the first two scenarios is correct regarding the y-intercept of $30:***
- Juan starts with $30 in savings and increases his savings amount by $5 each week.
- Juan starts with $30 in savings and increases his savings amount by $1 each week.
If you need to choose just one scenario with a stronger emphasis on savings being incremented regularly, the first option might be the most intuitive as it suggests a higher increase over time.
Answered by
GPT-4o mini
Given the information you've provided:
- The y-axis represents the savings amount, increasing in multiples of 10 up to 90.
- The x-axis represents time in weeks.
- After 4 weeks, Juan has $50 in savings.
From this, we can calculate the weekly savings increase.
1. **Starting Amount**: We still have the understanding that Juan starts with $30, as determined before.
2. **Amount After 4 Weeks**: Juan has $50.
3. **Calculate Total Increase in 4 Weeks**:
- Total amount gained in 4 weeks = $50 - $30 (initial savings) = $20.
4. **Weekly Savings Increase**:
- Weekly increase = Total increase / Number of weeks = $20 / 4 weeks = $5 per week.
Now we can set up the linear equation representing Juan's savings:
- Starting amount (y-intercept) = $30
- Increase per week (slope) = $5
So the equation for Juan's savings is:
\[ y = 30 + 5x \]
Where:
- \( y \) is the total savings after \( x \) weeks.
### Confirming the Scenario:
Using the equation, we can check the savings at various points:
- **At Week 0 (Start)**:
- \( y = 30 + 5(0) = 30 \)
- **At Week 1**:
- \( y = 30 + 5(1) = 35 \)
- **At Week 2**:
- \( y = 30 + 5(2) = 40 \)
- **At Week 3**:
- \( y = 30 + 5(3) = 45 \)
- **At Week 4**:
- \( y = 30 + 5(4) = 50 \)
This confirms that after 4 weeks, Juan indeed has $50 in savings based on the equation derived from the information provided.
### Conclusion:
The best scenario that describes the graph based on your inputs is:
- Juan starts with $30 in savings and increases his savings amount by $5 each week.
The graph would show a straight line starting at $30 and increasing by $5 for each subsequent week, consistent with the data provided.
- The y-axis represents the savings amount, increasing in multiples of 10 up to 90.
- The x-axis represents time in weeks.
- After 4 weeks, Juan has $50 in savings.
From this, we can calculate the weekly savings increase.
1. **Starting Amount**: We still have the understanding that Juan starts with $30, as determined before.
2. **Amount After 4 Weeks**: Juan has $50.
3. **Calculate Total Increase in 4 Weeks**:
- Total amount gained in 4 weeks = $50 - $30 (initial savings) = $20.
4. **Weekly Savings Increase**:
- Weekly increase = Total increase / Number of weeks = $20 / 4 weeks = $5 per week.
Now we can set up the linear equation representing Juan's savings:
- Starting amount (y-intercept) = $30
- Increase per week (slope) = $5
So the equation for Juan's savings is:
\[ y = 30 + 5x \]
Where:
- \( y \) is the total savings after \( x \) weeks.
### Confirming the Scenario:
Using the equation, we can check the savings at various points:
- **At Week 0 (Start)**:
- \( y = 30 + 5(0) = 30 \)
- **At Week 1**:
- \( y = 30 + 5(1) = 35 \)
- **At Week 2**:
- \( y = 30 + 5(2) = 40 \)
- **At Week 3**:
- \( y = 30 + 5(3) = 45 \)
- **At Week 4**:
- \( y = 30 + 5(4) = 50 \)
This confirms that after 4 weeks, Juan indeed has $50 in savings based on the equation derived from the information provided.
### Conclusion:
The best scenario that describes the graph based on your inputs is:
- Juan starts with $30 in savings and increases his savings amount by $5 each week.
The graph would show a straight line starting at $30 and increasing by $5 for each subsequent week, consistent with the data provided.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.