Finding the gradient from two points
Although it is sometimes easier to find the gradient of a lineby drawing a graph, it's not always necessary. The gradient (or steepness) of a line is the change in y divided by the change in x. If we are given two points on a line, we can find the difference between the x and y values, and therefore calculate the gradient.
For example, from the point (2, 3) to the point (4, 7), the x coordinate has increased by 2 and the y coordinate has increased by 4. The gradient is 4 divided by 2, which is 2.
It is important to always work from the same point for both x and y values, particularly for negative gradients. For example, from the point (6, 2) to the point (3, 11), the x coordinate decreases by 3, so the change in x is written as -3. The change in y is 9, so the gradient is 9 divided by -3, which is -3.