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:
- At \( m = 0 \) (the start), there are \( n = 2 \) employees.
- 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. \( n = \frac{5}{6}m + 2 \)
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