Gradient (Slope) of a Straight Line

The gradient (also called slope) of a line tells us how steep it is.

To find the gradient:

Divide the vertical change (how far it goes up or down) by the horizontal change (how far it moves sideways).

Gradient = Change in YChange in X

Have a play (drag the points):

geometry/images/geom-line-equn.js?mode=slope

Examples:

The gradient = 3 3 = 1

So the gradient is equal to 1

		The gradient = 4 2 = 2
The line is steeper, and so the gradient is larger.

		The gradient = 3 5 = 0.6
The line is less steep, and so the gradient is smaller.

Moving from left-to-right, the cyclist has to :

negative slope zero slope positive slope

When measuring the line:

Starting from the left and going across to the right is positive
(but going across to the left is negative).
Up is positive, and down is negative

Gradient = −4 2 = −2

That line goes down as you move along, so it has a negative gradient.

Gradient = 0 5 = 0

A line that goes straight across (horizontal) has a gradient of zero.

Gradient = 3 0 = undefined

That last one is a bit tricky ... you can't divide by zero,
so a "straight up and down" (vertical) line's gradient is "undefined".

We also call the horizontal change "run", and the vertical change "rise" or "fall":

rise and run

They are just different words, none of the calculations change.

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