Question

What does a gradient of ½ mean​

Answer 1

The gradient of ½ represents the slope or steepness of a line. In this case, a gradient of ½ means that for every 1 unit you move horizontally along the line, you will move ½ unit vertically.

To illustrate this, let's consider a line with a gradient of ½. If we start at the point (0, 0), for every 1 unit we move to the right, we would move ½ unit up. So, if we move 1 unit to the right, we would end up at the point (1, ½). If we move 2 units to the right, we would end up at the point (2, 1).

Alternatively, if we move 1 unit to the left, we would move ½ unit down. So, if we move 1 unit to the left from the starting point (0, 0), we would end up at the point (-1, -½). If we move 2 units to the left, we would end up at the point (-2, -1).

In summary, a gradient of ½ means that the line is inclined at an angle where for every 1 unit you move horizontally, you move ½ unit vertically.

Answer 2

A gradient of ½ refers to the rate at which a quantity is changing. In mathematics, a gradient represents the slope of a line or the rate of change between two points.

Explanation:

A gradient of ½ refers to the rate at which a quantity is changing. In mathematics, a gradient represents the slope of a line or the rate of change between two points.

If a gradient of ½ is given, it means that for every 1 unit increase in the independent variable (such as time, distance, or another quantity), the dependent variable (the quantity being measured or observed) increases by ½ unit.

For example, let's say we have a graph that represents the distance traveled by a car over time. If the gradient of ½ is given, it means that for every 1 hour increase in time, the car travels a distance of ½ mile.

In another scenario, if we have a gradient of ½ in a physics problem involving velocity, it means that for every 1 unit increase in time, the velocity increases by ½ unit.

In general, a gradient of ½ represents a positive but relatively slow rate of change. The larger the gradient, the steeper the line or the faster the rate of change.