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

Answer:

y=250x+300

Step-by-step 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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of line is

$y-4050=\frac{6550-4050}{25-15}(x-15)$

$y-4050=\frac{2500}{10}(x-15)$

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

$y-4050=250x-3750$

Add 4050 on both sides.

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

$y=250x+300$

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