express the cost as a linear function of the number of heaters ,x.

Question

A company finds it can produce 25 heaters for $7000​, while producing 35 heaters costs $9600. Express the​ cost, y, as a linear function of the number of​ heaters, x. Determine the cost to produce 40 heaters.

y=

Answer 1

y = mx + b where b is the starting point, in this case something like the cost of equipment, rent, the factory etc.

m is the slope, which is the additional cost per something, in this case per heater.

Slope is change in y / change in x = (9600-7000)/(35-25) = 2600/10 = 260 per heater

y = 260x + b where x is the number of heaters, and b is the starting cost.

Find b using the known cost for either number of heaters.

25: 7000 = 260*25 + b

7000 = 6500 + b

500 = b

35 will give the same answer for b: 9600 = 260*35 + b

9600 = 9100 + b

500 = b

The function is y = 260x + 500 where x is the number of heaters and y is the total cost of production.

When x = 40, it's this: y = 260*40 + 500 = 10,900

Answer 2

Start with two-point form:

(y - 7000) / (x - 25) = (7600 - 7000) / (35 - 25)

Can you conver to slope-intercept form and answer?