A software company started with 2 employees. In 6 months, the company had 14 employees. The number of employees increased at a steady rate.

a. create 2 ordered pairs.
b. find the slope.
c. Interpret the meaning of the slope.
d. Find the prediction equation.

a. At the start, months = 0; employees = 2. In 6 months, months = 6; employees =14

(0,2)
(6,14)

b and c. 2 employees/month is the slope
This is how many employees the company would have to add per month to get 14 employees at the end of 6 months

E = 2 + r*m
where E is the number of empoyees, r is the rate per month at which employees are added, and m is the number of months.

To create two ordered pairs, we need to identify the starting and ending points of the employee count over the given time period.

a. The starting number of employees is 2, and after 6 months, it increased to 14. Therefore, the two ordered pairs can be written as (0, 2) and (6, 14), representing the (time, number of employees).

b. To find the slope, we use the formula: slope = (change in y)/(change in x). In this case, the change in y is 14 - 2 = 12, and the change in x is 6 - 0 = 6. Therefore, the slope is 12/6 = 2.

c. The slope represents the rate at which the number of employees is changing per unit of time. In this case, since the slope is positive (2), it indicates that the number of employees is increasing steadily by 2 for every 1 unit of time.

d. To find the prediction equation, we can use the slope-intercept form of a linear equation: y = mx + b, where y represents the number of employees, x represents time, m is the slope, and b is the y-intercept.

Using the given information, we can substitute one of the ordered pairs (0, 2) into the equation and solve for the y-intercept (b):
2 = 2(0) + b
2 = b

Therefore, the prediction equation for the number of employees (y) over time (x) is:
y = 2x + 2