1. State the problem: Find the gradient (slope) of the line passing through points A(1,3) and B(-2,5). 2. Use the slope formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ 3. Substitute the given points: $x_1=1$, $y_1=3$, $x_2=-2$, $y_2=5$ into the formula: $$ m = \frac{5 - 3}{-2 - 1} = \frac{2}{-3} $$ 4. Simplify the fraction: $$ m = -\frac{2}{3} $$ 5. Conclusion: The gradient of the line through points A and B is $-\frac{2}{3}$.