SOLUTION: The first month a company was open, it had 2 employees. At the end of 6 months, the company had 10 employees. If the number of employees increases at a steady rate, write an equati

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The first month a company was open, it had 2 employees. At the end of 6 months, the company had 10 employees. If the number of employees increases at a steady rate, write an equati      Log On


   

Question 1055390: The first month a company was open, it had 2 employees. At the end of 6 months, the company had 10 employees. If the number of employees increases at a steady rate, write an equation that illustrates this situation.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot +t+ = time in months on the horizontal axis
Plot +E+ = the number of employees at the end
of +t+ months on the vertical axis
-------------------------------------------------
You are given 2 points on a straight line:
( t,E ) = ( 1, 2 ) and ( 6, 10 )
Use the general point-slope formula
+%28+E+-+2+%29+%2F+%28+t+-+1+%29+=+%28+10+-+2+%29+%2F+%28+6+-+1+%29+
+%28+E+-+2+%29+%2F+%28+t+-+1+%29++=+8%2F5+
Multiply both sides by +5%2A%28+t-1+%29+
+5%2A%28+E+-+2+%29+=+8%2A%28+t+-+1+%29+
+5E+-+10+=+8t+-+8+
+5E+=+8t+%2B+2+
+E+=+%288%2F5%29%2At+%2B+2%2F5+
----------------------------
check answer:
Does it go through ( 1,2 ) ?
+E+=+%288%2F5%29%2At+%2B+2%2F5+
+2+=+%288%2F5%29%2A1+%2B+2%2F5+
+2+=+8%2F5+%2B+2%2F5+
+2+=+2+
----------------------------
Does it go through ( 6, 10 )
+E+=+%288%2F5%29%2At+%2B+2%2F5+
+10+=+%288%2F5%29%2A6+%2B+2%2F5+
+10+=+48%2F5+%2B+2%2F5+
+10+=+50%2F5+
+10+=+10+
OK