Determine the gradient of a straight line
The gradient of a straight line is how steep it is. It can be calculated from a given set of coordinate points. There are three special cases of straight lines: parallel, horizontal and vertical.
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Gradient of a straight line
The gradient tells us how steep a line is, therefore the bigger the gradient the steeper the line is.
A positive gradient is a straight line which slopes up to the right.
A negative gradient is a straight line which slopes down to the right.
The gradient formula with coordinates
The gradient of the line joining \(A({x_1},{y_1})\) to \(B({x_2},{y_2})\) is written \({m_{AB}}\).
\[{m_{AB}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]