## Answer :

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.