Slope (Gradient) of a Straight Line

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


To calculate the Slope:

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

Have a play (drag the points):



gradient 3/3  

The Slope of this line = 3 3 = 1

So the Slope is equal to 1



The Slope of this line = 4 2 = 2

The line is steeper, and so the Slope is larger.


gradient 3/5  

The Slope of this line = 3 5 = 0.6

The line is less steep, and so the Slope is smaller.


Positive or Negative?

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

negative slope   zero slope   positive slope

When measuring the line:


gradient -4/2  

Slope = −4 2 = −2

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

Straight Across

gradient 0/5  

Slope = 0 5 = 0

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

Straight Up and Down

gradient 3/0  

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":

rise and run

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


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