According to Hooke's Law, a linear relationship exists between the distance that a spring stretches and the force stretching it. Suppose a weight of \( 0.5 \) kilograms causes a spring to stretch \( 2.75 \) centimeters and a weight of \( 1.2 \) kilograms causes the same spring to stretch \( 6.6 \) centimeters.

(a) Find a linear model that relates the distance \( d \) of the stretch and the weight w.

(b) What stretch is caused by a weight of \( 2.4 \) kilograms?

(c) What weight causes a stretch of \( 15.4 \) centimeters?