Gradient (Slope) of a Straight Line

The Gradient (also called Slope) of a straight line shows how steep a straight line is.


To calculate the Gradient:

Divide the change in height by the change in horizontal distance
Gradient = Change in YChange in X   gradient



The Gradient of this line = 3 3 = 1

So the Gradient is equal to 1



The Gradient of this line = 4 2 = 2

The line is steeper, and so the Gradient is larger.



The Gradient of this line = 3 5 = 0.6

The line is less steep, and so the Gradient is smaller.


Positive or Negative?




Gradient = −4 2 = −2

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

Straight Across


Gradient = 0 5 = 0

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

Straight Up and Down


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".

Rise and Run

Sometimes the horizontal change is called "run", and the vertical change is called "rise" or "fall":


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