1. **State the problem:** Find the equation of the line AB given points A(-1, 3) and B(5, 6), and find the coordinates of point P that divides AB in the ratio 2:1. 2. **Find the equation of line AB:** The slope $m$ of line AB is given by $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 3}{5 - (-1)} = \frac{3}{6} = \frac{1}{2}$$ 3. Use point-slope form with point A: $$y - 3 = \frac{1}{2}(x - (-1))$$ $$y - 3 = \frac{1}{2}(x + 1)$$ 4. Simplify to slope-intercept form: $$y = \frac{1}{2}x + \frac{1}{2} + 3 = \frac{1}{2}x + \frac{7}{2}$$ 5. **Find coordinates of P dividing AB in ratio 2:1:** Using section formula for internal division: $$x_P = \frac{2 \times 5 + 1 \times (-1)}{2 + 1} = \frac{10 - 1}{3} = \frac{9}{3} = 3$$ $$y_P = \frac{2 \times 6 + 1 \times 3}{2 + 1} = \frac{12 + 3}{3} = \frac{15}{3} = 5$$ 6. Therefore, coordinates of P are $(3, 5)$. **Final answers:** - Equation of line AB: $y = \frac{1}{2}x + \frac{7}{2}$ - Coordinates of P: $(3, 5)$