Slope (Gradient) of a Straight Line

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

Calculate

To calculate the Slope:

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

Examples:

 

The Slope of this line = 3 3 = 1

So the Slope is equal to 1

 

graph  

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.

 

Positive or Negative?

Important:

 

 

Slope = −4 2 = −2

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

Straight Across

 

Slope = 0 5 = 0

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

Straight Up and Down

11  

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".

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.