Question

A company has a manufacturing plant that is producing quality jackets. They find that in order to produce 150 jackets in a month, it will cost $5500. Also , to produce 370 jackets in a month , it will cost $8580 . Find an equation in the form y = mx + b , where is the number of jackets produced in a month and y is the monthly cost to do so.

Answer 1

`y = 14x + 3400`

Explanation:

Represent

- number of jackets with x

- costs of jackets with y

So, we have:

`(x_1,y_1) = (150,5500)`

`(x_2,y_2) = (370,8580)`

Required

Write an equation in form of y = mx + b

First, we need to determine the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (8580 - 5500)/(370 - 150)`

`m = (3080)/(220)`

`m = 14\\`

The equation is calculated using:

`y-y_1 = m(x - x_1)`

Where

`m = 14\\`

`(x_1,y_1) = (150,5500)`

So, we have:

`y - 5500 = 14(x - 150)`

`y - 5500 = 14x - 2100`

Make y the subject

`y = 14x - 2100 + 5500`

`y = 14x + 3400`