EDEXCEL GCSE FOUNDATION MATHS - What is the Gradient

Edexcel GCSE Foundation Maths: What is Gradient?

The gradient of a line tells us how steep it is. It's a measure of how much the line goes up or down for every unit it goes across.

Visualizing Gradient:

Imagine walking along a hill. If the hill is steep, you have to work hard to climb. This is like a line with a high gradient. If the hill is gentle, you can walk easily. This is like a line with a low gradient.

Calculating Gradient:

To calculate the gradient, we use the following formula:

Gradient = (Change in y) / (Change in x)

Let's break this down:

• Change in y: This is the vertical distance between two points on the line.
• Change in x: This is the horizontal distance between the same two points.

Example:

Imagine a line passing through the points (1, 2) and (4, 8).

1. Find the change in y: 8 - 2 = 6
2. Find the change in x: 4 - 1 = 3
3. Calculate the gradient: 6 / 3 = 2

Therefore, the gradient of the line is 2.

Understanding the Sign of Gradient:

• Positive Gradient: The line slopes upwards from left to right.
• Negative Gradient: The line slopes downwards from left to right.
• Zero Gradient: The line is horizontal.
• Undefined Gradient: The line is vertical.

Key Points:

• Gradient is a measure of steepness.
• A higher gradient indicates a steeper line.
• Gradient can be positive, negative, zero, or undefined.
• Use the formula "Gradient = (Change in y) / (Change in x)" to calculate gradient.

Practice:

Try calculating the gradient of the following lines:

1. A line passing through (2, 3) and (5, 9)
2. A line passing through (-1, 4) and (3, -2)

Understanding the concept of gradient will help you solve a variety of problems in Edexcel GCSE Foundation Maths.