What is the formula for calculating gradient from coordinates?

The formula for calculating the gradient from coordinates is: \((y_2 - y_1) / (x_2 - x_1)\).

To understand this better, let's break it down. The gradient (or slope) of a line measures how steep the line is. It is calculated by finding the change in the y-coordinates (vertical change) and dividing it by the change in the x-coordinates (horizontal change) between two points on the line.

Imagine you have two points on a graph: \((x_1, y_1)\) and \((x_2, y_2)\). The gradient \(m\) is found using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here’s a step-by-step guide:
1. Identify the coordinates of the two points. For example, let’s say the points are \((2, 3)\) and \((5, 11)\).
2. Subtract the y-coordinate of the first point from the y-coordinate of the second point: \(11 - 3 = 8\).
3. Subtract the x-coordinate of the first point from the x-coordinate of the second point: \(5 - 2 = 3\).
4. Divide the difference in y-coordinates by the difference in x-coordinates: \(8 / 3\).

So, the gradient \(m\) is \(\frac{8}{3}\) or approximately 2.67.

This formula is essential in GCSE Maths as it helps you understand the relationship between two points on a graph and how steep the line connecting them is. It’s a fundamental concept in coordinate geometry and is widely used in various applications, from simple graph plotting to more complex analyses in different fields.