Question

A company finds it can produce 5 heaters for $1750, while producing 10 heaters cost $3000. Express the cost, y, as a linear function of the number of heaters, x.

Answer 1

The cost function is linear, and as such has a slope and a y-intercept.

Two points on this line are (5, $1750) and (10, $3000).  As the number of heaters produced increases from 5 to 10, the production costs increase by $1250.  Thus, the slope of this line is m = $1250/5, or m = $250/unit.

Inserting known data into the slope-intercept form of the equation of a straight line, we get:

$3000 = ($250/unit)(10) + b.  Then $500 = b, and the cost function is:

y = ($250/unit)(x) + $500.