1. The problem asks to find the gradient of the line passing through the points (1,1) and (5,5). 2. The formula for the gradient (slope) $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Substitute the given points into the formula: $$m = \frac{5 - 1}{5 - 1}$$ 4. Simplify the numerator and denominator: $$m = \frac{4}{4}$$ 5. Cancel the common factor 4: $$m = \frac{\cancel{4}}{\cancel{4}} = 1$$ 6. Therefore, the gradient of the line is $1$. This means the line rises 1 unit vertically for every 1 unit it moves horizontally, confirming the positive slope shown in the graph.