Question

The number of employees a company had when it began 10 years ago was 13,000. Today, the company has 15,000 employees. The growth in the number of employees can be modeled by the graphed linear function, where x represents the number of years the company has been in business and y represents the number of employees. Which equations or functions represent the company's growth? Check all that apply.

y – 15,000 = 200(x – 10)
y – 13,000 = 200x
y – 13,000 = 10(x – 15,000)
f(x) = 200x + 13,000
f(x) = 200x – 13,000

Answer 1

a linear equation is in the form of y=mx+b
where m is the slope and b is the y-intercept
y intercept is the place on the y-axis where the function hits or when x=0

So we know two point on our graph:
1) when the company started there were 13,000 employees so at x=0 then y=13,000 Hence we have a point (0,13000)
2) we know that 10 years later we have 15,000 employees so at x=10 then y=15,000
Hence we have a point at (10,15,000)

Our slope is change of y divided by change of x
\[ m=\frac{15,000-13,000}{10-0}=\frac{2000}{10}=200\]
So our slope is divided by 200

Our y intercept is basically occurs when x=0 or where teh graph hits on the y-axis
In this case at x=0 then y=13,000 so our y-intercept is 13,000

Using the above information our equation looks as follows:
y=200x+13,000