Question

A company has a manufacturing plant that is producing quality canisters. They find that in order to produce 300 canisters in a month, it will cost $7400. Also, to produce 310 canisters in a month, it will cost $7550. Find an equation in the form y = mx + b, where r is the number of canisters produced in a month and y is the monthly cost to do so.

Answer: y =______

Answer 1

`y = 15x + 2900`

Explanation:

Given:

A company has find that in order to produce 300 canisters in a month, it will cost $7400. Also, to produce 310 canisters in a month, it will cost $7550.

Let
`x_(1)=300`,
`y_(1)=7400`,
`x_(2)=310`, and
`y_(2)=7550`

Find an equation in the form
`y = mx + b`------(1)

where x is the number of canisters produced in a month and y is the monthly cost to do

we know slope of line m =
`(y_(2)-y_(1))/(x_(2)-x_(1))`

Put all required value in above equation.

m =
`(7550-7400)/(310-300)`

m =
`(150)/(10)`

`m=15`

Put m value in equation 1.

`y = 15x + b`

For b we put
`y=7400` and
`x=300` in above equation.

`7400 = 15* 300 + b`

`7400 = 4500 + b`

`7400 - 4500 = b`

`b=2900`

Put m and b value in equation 1.

`y = 15x + 2900`

Therefore, the equation is
`y = 15x + 2900`