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Sagot :
To interpret the given question, it seems that we are dealing with comparing two different jobs based on their linear characteristics.
To adequately solve this, let's clarify the linear characteristics you typically need for point-slope form of a linear equation which is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where:
- [tex]\( m \)[/tex] is the slope,
- [tex]\( (x_1, y_1) \)[/tex] is a specific point on the line, often referred to as the [tex]$y$[/tex]-intercept in this context.
Let's break it down step by step for both jobs:
### 1. Amusement Park Job
Given:
- Nothing specific was given directly.
### 2. Tech Internship
Given:
- Nothing specific was given directly.
Since no specific values or additional information were provided within the table you provided, let's identify the constraints required:
Constraints Identification:
1. Slope [tex]\( m \)[/tex]:
- Both jobs need a determined slope. This typically could mean the rate at which earnings increase with respect to time or effort.
2. [tex]\( y \)[/tex]-intercept [tex]\((x_1, y_1)\)[/tex]:
- Both jobs need a defined starting point or baseline earning. Usually, at [tex]\( x = 0 \)[/tex], it could be initial pay when no work has been done.
3. Point-Slope form:
- This form expresses the job's earnings equation, which means we want to write the job's earnings model in the form [tex]\( y - y_1 = m(x - x_1) \)[/tex].
### Inferences:
1. Amusement Park Job:
- You will need the slope [tex]\( m \)[/tex] which might be the hourly wage.
- The [tex]\( y \)[/tex]-intercept [tex]\((x_1, y_1)\)[/tex] which could represent initial earnings before starting or any upfront payments.
2. Tech Internship:
- Similar to the amusement park, you will need a slope [tex]\( m \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\((x_1, y_1)\)[/tex].
### Example Solution Setup:
Let's assume hypothetical values to illustrate:
Amusement Park:
- Suppose the slope [tex]\( m \)[/tex] is 10 dollars/hour.
- Suppose [tex]\( y \)[/tex]-intercept is (0, 50) meaning initial payment is [tex]$50. Tech Internship: - Suppose the slope \( m \) is 20 dollars/hour. - Suppose \( y \)-intercept is (0, 100) meaning initial payment is $[/tex]100.
Using our assumptions, the equations would look like:
1. Amusement Park:
[tex]\[ y - 50 = 10(x - 0) \][/tex]
simplifying:
[tex]\[ y = 10x + 50 \][/tex]
2. Tech Internship:
[tex]\[ y - 100 = 20(x - 0) \][/tex]
simplifying:
[tex]\[ y = 20x + 100 \][/tex]
These equations represent potential earning models for each job where [tex]\( x \)[/tex] could be the number of hours worked, and [tex]\( y \)[/tex] the total pay.
### Conclusion:
The constraints needed to fill out the table are straightforward - values for the slope and [tex]\( y \)[/tex]-intercept for each job. Utilizing these, one can derive the equations depicting the earning models.
To adequately solve this, let's clarify the linear characteristics you typically need for point-slope form of a linear equation which is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where:
- [tex]\( m \)[/tex] is the slope,
- [tex]\( (x_1, y_1) \)[/tex] is a specific point on the line, often referred to as the [tex]$y$[/tex]-intercept in this context.
Let's break it down step by step for both jobs:
### 1. Amusement Park Job
Given:
- Nothing specific was given directly.
### 2. Tech Internship
Given:
- Nothing specific was given directly.
Since no specific values or additional information were provided within the table you provided, let's identify the constraints required:
Constraints Identification:
1. Slope [tex]\( m \)[/tex]:
- Both jobs need a determined slope. This typically could mean the rate at which earnings increase with respect to time or effort.
2. [tex]\( y \)[/tex]-intercept [tex]\((x_1, y_1)\)[/tex]:
- Both jobs need a defined starting point or baseline earning. Usually, at [tex]\( x = 0 \)[/tex], it could be initial pay when no work has been done.
3. Point-Slope form:
- This form expresses the job's earnings equation, which means we want to write the job's earnings model in the form [tex]\( y - y_1 = m(x - x_1) \)[/tex].
### Inferences:
1. Amusement Park Job:
- You will need the slope [tex]\( m \)[/tex] which might be the hourly wage.
- The [tex]\( y \)[/tex]-intercept [tex]\((x_1, y_1)\)[/tex] which could represent initial earnings before starting or any upfront payments.
2. Tech Internship:
- Similar to the amusement park, you will need a slope [tex]\( m \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\((x_1, y_1)\)[/tex].
### Example Solution Setup:
Let's assume hypothetical values to illustrate:
Amusement Park:
- Suppose the slope [tex]\( m \)[/tex] is 10 dollars/hour.
- Suppose [tex]\( y \)[/tex]-intercept is (0, 50) meaning initial payment is [tex]$50. Tech Internship: - Suppose the slope \( m \) is 20 dollars/hour. - Suppose \( y \)-intercept is (0, 100) meaning initial payment is $[/tex]100.
Using our assumptions, the equations would look like:
1. Amusement Park:
[tex]\[ y - 50 = 10(x - 0) \][/tex]
simplifying:
[tex]\[ y = 10x + 50 \][/tex]
2. Tech Internship:
[tex]\[ y - 100 = 20(x - 0) \][/tex]
simplifying:
[tex]\[ y = 20x + 100 \][/tex]
These equations represent potential earning models for each job where [tex]\( x \)[/tex] could be the number of hours worked, and [tex]\( y \)[/tex] the total pay.
### Conclusion:
The constraints needed to fill out the table are straightforward - values for the slope and [tex]\( y \)[/tex]-intercept for each job. Utilizing these, one can derive the equations depicting the earning models.
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