Gradient Calculator

How to Use the Gradient Calculator

The Gradient Calculator calculates the gradient (slope) of a line given two points on the line. Follow these steps to use the calculator:

1. Enter the x and y coordinates for the first point (x₁, y₁). For example, (3, 4).
2. Enter the x and y coordinates for the second point (x₂, y₂). For example, (7, 10).
3. Click the "Calculate" button. The calculator will compute the gradient using the formula:

Gradient (m) = (y₂ - y₁) / (x₂ - x₁)

4. The result will be displayed in the "Gradient (m)" field.
5. If the line is vertical (x₁ = x₂), the calculator will indicate that the gradient is undefined.

Understanding the Gradient (Slope)

The gradient (or slope) of a line is a measure of its steepness. It is defined as the change in the y-coordinate divided by the change in the x-coordinate between two points on the line. A positive gradient indicates an upward slope, while a negative gradient indicates a downward slope.

For example, if you have two points (2, 3) and (4, 7), the gradient would be:

Gradient (m) = (7 - 3) / (4 - 2) = 4 / 2 = 2

This means that for every unit increase in the x-coordinate, the y-coordinate increases by 2 units.