What is the gradient of the line passing through (1, 2) and (3, 6)?

The gradient of the line passing through (1, 2) and (3, 6) is 2.

To find the gradient of a line, we use the formula: \[ \text{Gradient} = \frac{\text{change in } y}{\text{change in } x} \]. This formula calculates how much the y-coordinate changes for a given change in the x-coordinate between two points on the line.

For the points (1, 2) and (3, 6), we first identify the coordinates: \((x_1, y_1) = (1, 2)\) and \((x_2, y_2) = (3, 6)\). Next, we calculate the change in y, which is \(y_2 - y_1 = 6 - 2 = 4\). Similarly, we calculate the change in x, which is \(x_2 - x_1 = 3 - 1 = 2\).

Now, we substitute these values into the gradient formula: \[ \text{Gradient} = \frac{4}{2} = 2 \]. Therefore, the gradient of the line is 2.

This means that for every unit increase in the x-coordinate, the y-coordinate increases by 2 units. The gradient tells us how steep the line is; a gradient of 2 indicates a relatively steep incline. Understanding how to calculate and interpret the gradient is crucial in GCSE Maths, as it helps in graphing linear equations and analysing the relationship between variables.