What is the gradient of a line with equation y = -2x + 4?

The gradient of the line with equation \( y = -2x + 4 \) is -2.

In the equation of a straight line, which is typically written in the form \( y = mx + c \), the gradient (or slope) is represented by the coefficient \( m \). This coefficient tells us how steep the line is and the direction it goes. In the given equation \( y = -2x + 4 \), the coefficient of \( x \) is -2. Therefore, the gradient of the line is -2.

The gradient is a measure of how much the \( y \)-value changes for a given change in the \( x \)-value. Specifically, a gradient of -2 means that for every 1 unit increase in \( x \), the \( y \)-value decreases by 2 units. This negative gradient indicates that the line slopes downwards from left to right.

Understanding the gradient is crucial for analysing the behaviour of linear functions. A positive gradient means the line slopes upwards, while a negative gradient means it slopes downwards. A gradient of zero would mean the line is horizontal, indicating no change in \( y \) as \( x \) changes.

In summary, the gradient of -2 in the equation \( y = -2x + 4 \) tells us that the line is decreasing and that it falls 2 units vertically for every 1 unit it moves horizontally to the right. This concept is fundamental in GCSE Maths and helps in graphing and interpreting linear relationships.