word problems

Question

A company has a manufacturing plant that is producing quality canisters. They find that in order to produce 200 canisters in a month, it will cost $9500. Also, to produce 370 canisters in a month, it will cost $13750. Find an equation in the form
y=mx+b,where x is the number of canisters produced in a month and
y is the monthly cost to do so.

Answer:

Answer 1

We have two points: (200, 9500), (370, 13750)

 

Find the slope:  m = (13750-9500)/(370-200) = 4250/170 = 25

 

y = 25x + b

Use one of the points as (x, y) to solve for b

9500 = 25(200) + b

b = 9500 - 5000 = 4500

 

y = 25x + 4500