Monday, February 24, 2020

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

Have a play (drag the points):

slope = 36 = 0.5

The Slope of this line = 33 = 1
So the Slope is equal to 1

		The Slope of this line = 42 = 2
The line is steeper, and so the Slope is larger.

		The Slope of this line = 35 = 0.6
The line is less steep, and so the Slope is smaller.

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

Slope = −42 = −2

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

Slope = 05 = 0

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

Slope = 30 = 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".

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.