What is the gradient of a line perpendicular to y = x - 2?

The gradient of a line perpendicular to \( y = x - 2 \) is \( -1 \).

To understand why, let's start by looking at the gradient of the given line. The equation \( y = x - 2 \) is in the form \( y = mx + c \), where \( m \) represents the gradient. In this case, the gradient \( m \) is 1.

When two lines are perpendicular, the product of their gradients is always -1. This is a key property of perpendicular lines. So, if the gradient of one line is \( m \), the gradient of the line perpendicular to it will be \( -\frac{1}{m} \).

For the line \( y = x - 2 \), the gradient \( m \) is 1. To find the gradient of the perpendicular line, we use the formula \( -\frac{1}{m} \). Substituting \( m = 1 \) into the formula gives us \( -\frac{1}{1} = -1 \).

Therefore, the gradient of a line perpendicular to \( y = x - 2 \) is \( -1 \). This means that if you were to draw a line with a gradient of -1, it would intersect the line \( y = x - 2 \) at a right angle, forming a perfect 90-degree angle.