Gradients

The gradient, m, of a line is also known as the slope of the line. This is defined by:

$m = \dfrac{rise}{run}$
Where the rise is the increase in the vertical axis (y), and the run is increase in the horizontal axis (x). This is demonstrated below:

Since the rise and run are taken to be the differences between the two points, then the gradient can also be defined as:

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

When finding the equation of a straight line, sometimes it is convenient to rearrange this so that it is in the form:

$y_2 - y_1 = m(x_2 - x_1)$

See also:

Equation for a straight line

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