The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4000 to produce 300 chairs in one day. (a) assuming that the relationship between cost c and the number of chairs produced x is linear, find an equation that expresses this relationship.

C - cost;  x - the number of chairs produced;
Linear equation: y = m x + b  ( m = ?, b = ? )
2200  = 100 m  + b  / * ( -1 )(we will multiply both sides of the equation by -1) 
4000 = 300 m + b

- 2200 = - 100 m - b
+
 4000 =  300 m + b

1800 = 200 m
m = 1800 : 200 ,  m = 9 ( we will then plug in the first equation )
2200 = 9 * 100 + b
2200 = 900 + b
b = 2200 - 900,  m = 1300
 C = 9 x + 1300