What is the gradient of the line y = -2x + 7?

The gradient of the line \( y = -2x + 7 \) 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 \( y = -2x + 7 \), 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 unit change in the \( x \)-value. A negative gradient, like -2 in this case, means that the line slopes downwards from left to right. For every 1 unit increase in \( x \), the \( y \)-value decreases by 2 units. This is why the line goes down as you move along the \( x \)-axis.

Understanding the gradient is crucial because it helps you determine the direction and steepness of the line. If the gradient were positive, the line would slope upwards. If the gradient were zero, the line would be horizontal, indicating no change in \( y \) as \( x \) changes. In summary, the gradient of -2 tells us that the line is quite steep and descends as you move from left to right on the graph.