Question

A software company started with 2 employees. In 6 months the company had 7 employees. The number of employees increased at a steady rate. Which equation models the relationship between the number of employees n and the number of months m since the company started?

A. N=5/6m + 2
B. M= 2n + 5/6
C. N=6/5m + 2
D. M= 5/6n + 2

Answer 1

To model the relationship between the number of employees \( n \) and the number of months \( m \) since the company started, we can analyze the data provided:

1. At \( m = 0 \) (the start), there are \( n = 2 \) employees.
2. At \( m = 6 \) months, there are \( n = 7 \) employees.

This indicates an increase of:

\[ 7 - 2 = 5 \text{ employees over } 6 \text{ months}. \]

To find the rate of change of the number of employees per month, we calculate:

\[ \text{Rate} = \frac{\Delta n}{\Delta m} = \frac{5}{6}. \]

This means that for each month, the number of employees increases by \( \frac{5}{6} \).

Now, we can use the point-slope form of the linear equation. The general equation for a line in this context is given by:

\[
n = \text{slope} \cdot m + \text{intercept}.
\]

Here, the slope (rate of change) is \( \frac{5}{6} \) and the y-intercept (initial number of employees when \( m = 0 \)) is \( 2 \). Thus, we can write the equation as:

\[
n = \frac{5}{6}m + 2.
\]

However, we need to express it in the correct format matching the provided options.

By rearranging, we see:

To compare options:

- A. \( n = \frac{5}{6}m + 2 \)
- B. \( m = 2n + \frac{5}{6} \) (not correct)
- C. \( n = \frac{6}{5}m + 2 \) (not correct)
- D. \( m = \frac{5}{6}n + 2 \) (not correct)

Thus, the correct equation that models the relationship between the number of employees \( n \) and the number of months \( m \) is:

**A. \( n = \frac{5}{6}m + 2 \)**