1. The problem is to find the formula for the gradient (slope) of a line given two points or a function. 2. The gradient formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the rate of change of $y$ with respect to $x$. 3. Important rules: - The denominator $x_2 - x_1$ cannot be zero because division by zero is undefined. - The gradient tells us how steep the line is; positive means increasing, negative means decreasing. 4. If you have a function $y = f(x)$, the gradient at a point is the derivative $\frac{dy}{dx}$. 5. Example: For points $(2, 3)$ and $(5, 11)$, $$m = \frac{11 - 3}{5 - 2} = \frac{8}{3}$$ So the gradient is $\frac{8}{3}$. This completes the explanation of the gradient formula.