# Gradient (Slope) of a Straight Line

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

## Calculate

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

## Examples:

 The Gradient = 3 3 = 1 So the Gradient is equal to 1

 The Gradient = 4 2 = 2 The line is steeper, and so the Gradient is larger.

 The Gradient = 3 5 = 0.6 The line is less steep, and so the Gradient is smaller.

## Positive or Negative?

Going from left-to-right, the cyclist has to Push on a Positive Slope:

When measuring the line:

• Starting from the left 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.