What is the slope of the line with equation y = -5x + 8?

The slope of the line with equation y = -5x + 8 is -5.

In the equation y = -5x + 8, the slope is represented by the coefficient of x. This form of the equation is known as the slope-intercept form, which is written as y = mx + c. Here, m represents the slope, and c represents the y-intercept, which is the point where the line crosses the y-axis.

To understand the slope, think of it as a measure of how steep the line is. A positive slope means the line rises as it moves from left to right, while a negative slope means the line falls. In this case, the slope is -5, indicating that for every unit you move to the right along the x-axis, the line falls by 5 units. This steep negative slope shows a rapid decrease.

The y-intercept, which is 8 in this equation, tells us that the line crosses the y-axis at the point (0, 8). This is useful for graphing the line, as you can start at this point and use the slope to determine the direction and steepness of the line.

Understanding the slope and y-intercept helps you quickly sketch the graph of the line and analyse its behaviour. For GCSE Maths, mastering these concepts is crucial for solving various problems involving linear equations.