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The problem presents Dianelys' salary progression over time. It starts at $40,000 in the first year and increases by $2,500 every year. We are tasked with finding an equation for $ S $, Dianelys' salary after working $ n $ years, where $ n $ is the number of years at the company.

### Observing the table:

| Number of Years (n) | Salary (S)    |
|---------------------|---------------|
| 0                   | 40,000        |
| 1                   | 42,500        |
| 2                   | 45,000        |
| 3                   | 47,500        |

The salary increases by $2,500 each year, which suggests a linear relationship between $ S $ and $ n $.

The general form of a linear equation is:
\[
S = m n + b
\]
where:
- $ m $ is the rate of change (the annual raise, $2,500),
- $ b $ is the starting salary when $ n = 0 $, which is $40,000.

### Constructing the equation:

From the table, we know:
- $ m = 2500 $,
- $ b = 40,000 $.

Thus, the equation for Dianelys' salary after $ n $ years is:
\[
S = 2500n + 40000
\]

Would you like more details or have any other questions?

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Here are 5 related questions to consider:
1. How would Dianelys' salary change if her annual raise increased to $3,000?
2. What would Dianelys' salary be after 10 years of working at the company?
3. How can you graph this linear equation, and what does the slope represent?
4. What if Dianelys received a one-time bonus of $5,000 in her second year—how would that affect the equation?
5. Can you express the total earnings over $ n $ years using this equation?

**Tip**: In a linear equation, the coefficient of $ n $ (in this case, $2,500) represents the slope, or the rate of change. This tells you how much the dependent variable (salary) increases for each additional unit of the independent variable (years worked).

Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40,000, and she will receive a raise of $2,500 every year. Make a table of values and then write an equation for S, in terms of n, representing Dianelys' salary after working n years for the company.

Discover how to write a linear equation to represent Dianelys' salary progression with an annual raise. Starting with a base salary of $40,000, learn how her salary increases by $2,500 each year using the formula S = 2500n + 40000. Suitable for students in Grades 6-8.

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