Final answer:
The correct equation to describe the relationship between the number of employees y and the number of months x since the company started is y = 0.25x + 2, option (a). This reflects the initial count of 2 employees and an addition of 2 employees every 8 months.
Step-by-step explanation:
To find the equation that shows the relationship between the number of employees y and the number of months x since the company started, we need to determine the rate at which new employees are added and the initial number of employees.
The company starts with 2 employees, which is our initial value for y when x is 0. Since they add 2 new employees every 8 months, the rate of change in number of employees is 2 employees per 8 months. To find the slope (the rate at which employees increase per month), we divide the number of employees added by the time period: 2 employees / 8 months = 0.25 employees per month. This slope tells us how much the number of employees increases for each month that passes.
Therefore, the equation that represents this situation is y = 0.25x + 2, which correlates with option (a). Here the slope is 0.25, indicating the rate of employee increase per month, and the y-intercept is 2, indicating the initial number of employees.