What is the gradient of the line passing through (0, 0) and (4, 8)?

The gradient of the line passing through (0, 0) and (4, 8) is 2.

To find the gradient of a line, you need to determine the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. This is often referred to as "rise over run." The formula for the gradient (m) is:

\[ m = \frac{\Delta y}{\Delta x} \]

In this case, the two points given are (0, 0) and (4, 8). Let's label these points as \((x_1, y_1)\) and \((x_2, y_2)\) respectively. So, \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (4, 8)\).

Now, calculate the change in y-coordinates (\(\Delta y\)) and the change in x-coordinates (\(\Delta x\)):

\[ \Delta y = y_2 - y_1 = 8 - 0 = 8 \]
\[ \Delta x = x_2 - x_1 = 4 - 0 = 4 \]

Next, substitute these values into the gradient formula:

\[ m = \frac{8}{4} = 2 \]

Therefore, the gradient of the line passing through the points (0, 0) and (4, 8) is 2. This means that for every unit increase in the x-coordinate, the y-coordinate increases by 2 units. This is a key concept in understanding how steep a line is on a graph.