Question

A company started with 3 employees and after 8 months grew to 19. The growth was steady.

What is the equation that models the growth of the company's employees?

Answer 1

y = 2x + 3

Explanation:

We can make 2 coordinate points and find equation of the line using the line formula.

We can say that at starting (0 months), there were 3 employees.

After 8 months, there were 19 employees.

Let months be x points and number of employees be y points.

Thus, 2 points would be:

(0,3) & (8,19)

Now, the equation of the line is given as:

`y=mx+b`

Where m is the slope and b is the y-intercept

Let's find slope first with the formula:

`m=(y_2-y_1)/(x_2-x_1)`

Where

x_1 = 0

x_2 = 8

y_1 = 3

y_2 = 19

Thus, we have:

Slope =
`m=(y_2-y_1)/(x_2-x_1)=(19-3)/(8-0)=(16)/(8)=2`

Now we have:

y = 2x + b

To find b, we put (0,3) into the equation:

y = 2x + b

3 = 2(0) + b

3 = 0 + b

b = 3

So the equation of the line is:

y = 2x + 3