The gradient (also known as the slope) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:

\( \text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1} \(

Given the points \(P(1, 1)\) and \(Q(2, 5)\), we can plug in the coordinates into the formula:

\( \text{Gradient} = \frac{5 - 1}{2 - 1} = \frac{4}{1} = 4 \(

So, the gradient of the line passing through the points \(P(1, 1)\) and \(Q(2, 5)\) is 4.