(0.0 , 60000.0)  (1.0 , 40000.0)
How much does the line predict someone with 3 years of educational experience would make? Represent this as an ordered pair.

c) How much does the line predict someone with 4 years of educational experience would make? Represent this as an ordered pair.

d) Use the points you created in the previous two questions to find the slope of the trend line. Write the slope as a fraction.

e) Attach units to the slope in both the numerator and the denominator. Explain in a few sentences what information this rate is giving us.

Let's go through each part of the problem step by step.

### Given:
- Two points on the line: $(0.0, 60000.0)$ and $(1.0, 40000.0)$
  - These points represent the years of education (x) and corresponding salary (y).

---

### Part 1: **Find the predicted salary for someone with 3 years of education.**

We can model this situation using the equation of a line $ y = mx + b $, where:
- $ m $ is the slope of the line
- $ b $ is the y-intercept (initial salary when years of education = 0)

#### Step 1: Calculate the slope $m$

Using the two given points $(0.0, 60000.0)$ and $(1.0, 40000.0)$, the slope $ m $ is calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{40000 - 60000}{1.0 - 0.0} = \frac{-20000}{1.0} = -20000
\]

#### Step 2: Write the equation of the line

Since we have the slope $m = -20000$, and the y-intercept $b = 60000$ (from the point $(0, 60000)$), the equation of the line is:

\[
y = -20000x + 60000
\]

#### Step 3: Predict the salary for 3 years of education

Substitute $x = 3$ into the equation:

\[
y = -20000(3) + 60000 = -60000 + 60000 = 0
\]

Thus, for 3 years of education, the predicted salary is $0.

The ordered pair is: $\mathbf{(3, 0)}$

---

### Part 2: **Find the predicted salary for someone with 4 years of education.**

Substitute $x = 4$ into the equation $y = -20000x + 60000$:

\[
y = -20000(4) + 60000 = -80000 + 60000 = -20000
\]

Thus, for 4 years of education, the predicted salary is $-20000$ (which is likely unrealistic, but it follows from the mathematical model).

The ordered pair is: $\mathbf{(4, -20000)}$

---

### Part 3: **Find the slope of the trend line using the points from the previous two questions.**

We now use the points $(3, 0)$ and $(4, -20000)$ to find the slope.

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-20000 - 0}{4 - 3} = \frac{-20000}{1} = -20000
\]

Thus, the slope of the line is $ -20000 $.

---

### Part 4: **Attach units to the slope and explain its meaning.**

- **Numerator units (y-axis):** Dollars (salary)
- **Denominator units (x-axis):** Years of education

The slope is $ -20000 \, \text{dollars/year} $, meaning that for each additional year of education, the predicted salary decreases by $20,000. This negative trend indicates that the model predicts a decline in salary with more years of education (based on the given data).

---

Do you need more details on any part, or have any questions?

### Five Follow-Up Questions:
1. How does the y-intercept impact the salary prediction in this scenario?
2. Why does the model predict a decrease in salary with additional years of education?
3. How would the equation of the line change if the slope were positive?
4. What real-world factors might contradict this model’s prediction?
5. Could this model be used to predict salaries for more than 4 years of education? Why or why not?

### Tip:
Always analyze whether the results of a model are realistic in the context of the problem being solved, and adjust the model if necessary.

How much does the line predict someone with 3 years of educational experience would make? Represent this as an ordered pair. How much does the line predict someone with 4 years of educational experience would make? Represent this as an ordered pair. Use the points you created in the previous two questions to find the slope of the trend line. Write the slope as a fraction. Attach units to the slope in both the numerator and the denominator. Explain in a few sentences what information this rate is giving us.

Learn how to predict salaries using linear equations with slope-intercept form. The problem involves calculating the slope from given points and predicting salaries for 3 and 4 years of education. Suitable for Grades 8-10 students.

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