1. **State the problem:** Simplify the expression for $y$ given by $$y = \frac{3}{2} (-3 + t)$$. 2. **Formula and rules:** To simplify, use the distributive property: $$a(b + c) = ab + ac$$. 3. **Apply distributive property:** $$y = \frac{3}{2} \times (-3) + \frac{3}{2} \times t$$ 4. **Calculate each term:** $$y = -\frac{9}{2} + \frac{3}{2} t$$ 5. **Final simplified form:** $$y = \frac{3}{2} t - \frac{9}{2}$$ This is the simplified linear expression for $y$ in terms of $t$.