The gradient of a line describes how steep the line is. In the figure, line

The gradient of a line is defined as the ratio of the vertical distance to the horizontal distance. This can be understood by looking at the line as the hypotenuse of a right-angled triangle. Then the gradient is the ratio of the length of the vertical side of the triangle to the horizontal side of the triangle. Consider a line between a point

So we obtain the following for the gradient of a line:

We can use the gradient of a line to determine if two lines are parallel or perpendicular. If the lines are parallel (Figure 3a) then they will have the same gradient, i.e.

For example the gradient of the line between the points

The following video provides a summary of the gradient of a line.

Gradient of a line |
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