The distance d between the bottom of a suspended spring and a countertop is a linear function

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The distance d between the bottom of a suspended spring and a countertop is a linear function of the weight w attached to the bottom of the spring. The bottom of the spring is 9 inches from the countertop when the attached weight is 1.5 pounds and 5 inches from the countertop when the attached weight is 2.5 pounds.

(a) Find a linear model that relates the distance d from the countertop and the weight w.

(b) Find the distance between the bottom of the spring and the countertop if no weight is attached.

(c) What is the smallest weight that will make the bottom of the spring reach the countertop? (Ignore the thickness of the weight.)

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