Slope (Gradient) of a Straight Line

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

To find the slope:

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

Slope = Change in YChange in X

Have a play (drag the points):

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

Examples:

The slope of this line = 3 3 = 1

So the slope is equal to 1

In other words for every 3 steps right, the line goes up 3 steps. Since both are the same, the slope is 1.

		The slope of this line = 4 2 = 2
The line is steeper, and so the slope is larger.

		The slope of this line = 3 5 = 0.6
The line is less steep, and so the slope 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

Slope = −4 2 = −2

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

Slope = 0 5 = 0

A line that goes straight across (Horizontal) has a slope of zero.

Slope = 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 slope 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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