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
  gradient

Examples:

 
The Gradient of this line =
3
3
 =  1

So the Gradient is equal to 1


graph      
     
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

11      
     
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":

gradient

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