1. **State the problem:** Find the equation of the line passing through the points $(3, 3)$ and $(4, 6)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}.$$\n\n3. **Calculate the slope:** Substitute the points: $$m = \frac{6 - 3}{4 - 3} = \frac{3}{1} = 3.$$\n\n4. **Use point-slope form:** The equation of the line is $$y - y_1 = m(x - x_1).$$ Using point $(3, 3)$, we get $$y - 3 = 3(x - 3).$$\n\n5. **Simplify the equation:** $$y - 3 = 3x - 9.$$\n\n6. **Isolate $y$:** $$y = 3x - 9 + 3.$$\n\n7. **Final equation:** $$y = 3x - 6.$$\n\nThis is the equation of the line passing through the points $(3, 3)$ and $(4, 6)$.