Question
Anderson is a plumber and is paid a fixed amount just to make a house visit. The remainder of his fee, y, is determined by the number of hours that he works, x, as shown below.
Which equation represents the graph?
(1 point)
Responses
y=10x−50
y is equal to 10 x minus 50
y=50x+10
y is equal to 50 x plus 10
y=50x−10
y is equal to 50 x minus 10
y=10x+50
Which equation represents the graph?
(1 point)
Responses
y=10x−50
y is equal to 10 x minus 50
y=50x+10
y is equal to 50 x plus 10
y=50x−10
y is equal to 50 x minus 10
y=10x+50
Answers
GPT-4o mini
To determine which equation represents the graph of Anderson's fee structure, we need to consider the components of his pay: a fixed amount for the house visit and a charge based on the hours he works.
1. A fixed fee is usually represented as a constant in the equation (the y-intercept).
2. The variable fee based on hours worked is represented by the slope.
Given that the options have either positive or negative constants and slopes, we can analyze them based on typical components of such a fee structure:
- If the fixed amount is a positive value (let's assume it's $50, a common scenario), it will be the y-intercept.
- The hourly rate might be a positive value (for example, $10 per hour).
Based on this reasoning, among the options given:
1. **y = 10x - 50**:
- This suggests a fixed amount of -50, which doesn't make sense in a typical fee structure.
2. **y = 50x + 10**:
- This suggests a very large fee based on hours worked and a small fixed fee, which is unrealistic.
3. **y = 50x - 10**:
- Again, this suggests a large hourly fee, but with a fixed amount of -10, which is not typical for a service fee.
4. **y = 10x + 50**:
- This indicates a charge of $10 per hour plus a fixed fee of $50.
Based on this analysis, the most reasonable equation representing Anderson's fee structure, with a sensible fixed fee and an hourly charge, is:
**y = 10x + 50**.
This option fits the description best, assuming $50 is the base service fee and $10 an hourly rate for additional work.
1. A fixed fee is usually represented as a constant in the equation (the y-intercept).
2. The variable fee based on hours worked is represented by the slope.
Given that the options have either positive or negative constants and slopes, we can analyze them based on typical components of such a fee structure:
- If the fixed amount is a positive value (let's assume it's $50, a common scenario), it will be the y-intercept.
- The hourly rate might be a positive value (for example, $10 per hour).
Based on this reasoning, among the options given:
1. **y = 10x - 50**:
- This suggests a fixed amount of -50, which doesn't make sense in a typical fee structure.
2. **y = 50x + 10**:
- This suggests a very large fee based on hours worked and a small fixed fee, which is unrealistic.
3. **y = 50x - 10**:
- Again, this suggests a large hourly fee, but with a fixed amount of -10, which is not typical for a service fee.
4. **y = 10x + 50**:
- This indicates a charge of $10 per hour plus a fixed fee of $50.
Based on this analysis, the most reasonable equation representing Anderson's fee structure, with a sensible fixed fee and an hourly charge, is:
**y = 10x + 50**.
This option fits the description best, assuming $50 is the base service fee and $10 an hourly rate for additional work.