1. The problem is to prove that points lie on a line using the gradient (slope). 2. The formula for the gradient between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $m$ is the gradient. 3. To prove points are collinear, calculate the gradient between each pair of consecutive points. 4. If all gradients are equal, the points lie on the same straight line. 5. For example, given points $A(x_1, y_1)$, $B(x_2, y_2)$, and $C(x_3, y_3)$, calculate: - $m_{AB} = \frac{y_2 - y_1}{x_2 - x_1}$ - $m_{BC} = \frac{y_3 - y_2}{x_3 - x_2}$ 6. If $m_{AB} = m_{BC}$, then points $A$, $B$, and $C$ are collinear. 7. This method works because equal gradients mean the line connecting the points has the same slope, confirming they lie on the same straight line.