# 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
 Change in Y Change in X

## Examples:

The Gradient of this line =
 3 3
=  1

So the Gradient is equal to 1

 4 2
=  2

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

 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

 -4 2
= –2

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

## Straight Across

 0 5
=  0

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

## Straight Up and Down

 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