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

Question

A company finds it can produce 30 heaters for $8700​, while producing 40 heaters costs $11,400. Express the​ cost, y, as a linear function of the number of​ heaters, x. Determine the cost to produce 45 heaters.

y= _____

simplify your answer

Answer 1

As the relationship is linear, the graph would be a straight line in the form y = mx + b, where m is the slope, x is no. of units and b is the y-intercept. Could assume $'s on y-axis and units on x-axis.

Find the slope; rise/run or Δy/Δx = (11400 - 8700)/(40 - 30) = 2700/10 = $270/unit.

Now solve for by using one of the ordered pairs: 8700 = 270(30) + b → 8700 = 8100 + b

b = 8700 - 8100 = 600.

So y = 270x + 600

45 units would cost 270(45) + 600. Do the calculation.

Can check the equation:

If x = 30, y = 270(30) + 600 = $8700

If x = 40, y = 270(40) + 600 = $11400