Question

A spring has a length of 12 inches when a 2-pound weight is attached, and a length of 18 inches when a 5-pound weight is attached. Use rate of change to find the length of the spring when no weights are attached.

Answer 1

Let L be the length (in inches) and W the weight (in pounds). L depends linearly on W, so L = mW + b. The slope m = (18 − 12)/(5 − 2) = 6/3 = 2 inches per pound. Using (W,L) = (2,12): 12 = 2·2 + b so b = 8.

Thus the length with no weight (W = 0) is L(0) = b = 8 inches.