Question

A company finds it can produce 15 heaters for $ 4050​, while producing 25 heaters costs $ 6550. Express the​ cost, y, as a linear function of the number of​ heaters, x.

Answer 1

y=250x+300

Explanation:

Let x be the number of heaters and y be the total cost.

We need to find the linear function for y in terms of x.

It is given that company can produce 15 heaters for $4050 and 25 heaters costs $ 6550.

It means the line passes through the points (15,4050) and (25,6550).

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of line is

`y-4050=(6550-4050)/(25-15)(x-15)`

`y-4050=(2500)/(10)(x-15)`

`y-4050=250(x-15)`

`y-4050=250x-3750`

Add 4050 on both sides.

`y-4050+4050=250x-3750+4050`

`y=250x+300`

Therefore, the required linear function is y=250x+300.