equation that relates cost C and number of item x

[Algebragreek2me]

In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relastes C and x.

Our teacher says to show our work. I come up with:

100x+by=10000
300x+by= 22000

Are the equations right? And, if so, how do I show the work?

 

[skeeter]

you have a set of 2 ordered pairs (x, C) ...

(100, 10000) and (300, 22000)

rate of change (slope) = (22000 - 10000)/(300 - 100) = 12000/200 = 60

using the point-slope form of a linear equation ...

C - 10000 = 60(x - 100)

C = 60x + 4000