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

Answer:

$y = 14x + 3400$

Step-by-step 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)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{8580 - 5500}{370 - 150}$

$m = \frac{3080}{220}$

$m = 14$

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

$y = 14x - 2100 + 5500$

$y = 14x + 3400$