Question

In 2012, the average salary for a New York City Teacher was $58,240. Every year, the average salary increased at a constant rate. In 2019, the average salary was $67,060.
What is the slope or rate of change of this linear relationship?

Answer 1

To find the slope or rate of change of the average salary for New York City teachers, we can define the years and corresponding salaries as points on a graph:

- In 2012 (let's denote this as year 0), the average salary is $58,240.
- In 2019 (which is year 7, since 2019 - 2012 = 7), the average salary is $67,060.

The slope (rate of change) is calculated using the formula:

\[
\text{slope} = \frac{\text{change in salary}}{\text{change in years}} = \frac{S_2 - S_1}{T_2 - T_1}
\]

where:
- \( S_1 = 58,240 \) (salary in 2012)
- \( S_2 = 67,060 \) (salary in 2019)
- \( T_1 = 0 \) (corresponding year for 2012)
- \( T_2 = 7 \) (corresponding year for 2019)

Now we can plug in the values:

\[
\text{slope} = \frac{67,060 - 58,240}{7 - 0} = \frac{8,820}{7}
\]

Calculating that gives:

\[
\text{slope} = 1,260
\]

Therefore, the slope or rate of change of the average salary for New York City teachers is **$1,260 per year**.