1. **State the problem:** Find the point that is $\frac{1}{3}$ of the way from point A to point B, where A is at $(-3, -2)$ and B is at $(1, 5)$. 2. **Formula used:** The point $P$ that divides the segment from $A(x_1, y_1)$ to $B(x_2, y_2)$ in the ratio $m:n$ is given by: $$P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$$ Since we want the point $\frac{1}{3}$ of the way from $A$ to $B$, the ratio is $m:n = 1:2$ (because $1/3$ along means 1 part towards B and 2 parts remaining). 3. **Apply the formula:** $$x = \frac{1 \times 1 + 2 \times (-3)}{1+2} = \frac{1 - 6}{3} = \frac{-5}{3}$$ $$y = \frac{1 \times 5 + 2 \times (-2)}{1+2} = \frac{5 - 4}{3} = \frac{1}{3}$$ 4. **Intermediate step showing cancellation:** $$x = \frac{\cancel{1} - 6}{\cancel{3}} = -\frac{5}{3}$$ $$y = \frac{5 - \cancel{4}}{\cancel{3}} = \frac{1}{3}$$ 5. **Final answer:** The point $\frac{1}{3}$ of the way from $A$ to $B$ is: $$\boxed{\left(-\frac{5}{3}, \frac{1}{3}\right)}$$