1. **State the problem:** We are given a function $g(x) = x f(x)$, with $f(3) = 4$ and $f'(3) = -2$. We need to find the equation of the tangent line to the graph of $g$ at $x = 3$. 2. **Recall the formula for the tangent line:** The tangent line to $g$ at $x = a$ is given by $$y = g(a) + g'(a)(x - a)$$ where $g'(a)$ is the derivative of $g$ evaluated at $x = a$. 3. **Find $g'(x)$ using the product rule:** Since $g(x) = x f(x)$, $$g'(x) = f(x) + x f'(x)$$ (Product rule: derivative of first times second plus first times derivative of second.) 4. **Evaluate $g(3)$:** $$g(3) = 3 \times f(3) = 3 \times 4 = 12$$ 5. **Evaluate $g'(3)$:** $$g'(3) = f(3) + 3 \times f'(3) = 4 + 3 \times (-2) = 4 - 6 = -2$$ 6. **Write the equation of the tangent line:** $$y = g(3) + g'(3)(x - 3) = 12 - 2(x - 3) = 12 - 2x + 6 = 18 - 2x$$ **Final answer:** $$y = 18 - 2x$$