Gradient (Slope) of a Straight Line

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

Calculate

The method to calculate the Gradient is:

Divide the change in height by the change in horizontal distance

Gradient  =

Change in Y Change in X

Examples:

The Gradient of this line = 3 3  =  1 So the Gradient is equal to 1

	Gradient =	4 2	=  2

(The line is steeper, and so the Gradient is larger)

		Gradient =	3 5	=  0.6

(The line is less steep, and so the Gradient is smaller) 

Positive or Negative?

Important:

Starting from the left end of the line 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.

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

Video tutorial

The following are webpages that can assist you in the topics that were covered on this page:
 

http://www.purplemath.com/modules/slope.htm

http://www.math.com/school/subject2/lessons/S2U4L2DP.html

credit to :

http://www.mathsisfun.com/gradient.html
http://www.mathtutor.ac.uk