The gradient of a line provides a numerical value for the steepness of that line. It is calculated by taking the vertical change over the horizontal change between two points on the line. The gradient can be found from the coordinates of two points by using the formula: Gradient = Change in y / Change in x. This calculates the slope of the line formed by those two points. A negative gradient indicates a downward sloping or declining line.
1. The gradient of a line
The gradient of a line is a specific term for
the steepness of a straight line.
We all have an in-built sense of steepness
and can order the steepness of lines.
However, the gradient gives a numerical
value to this general understanding.
2. To calculate the gradient of a line we count
the vertical distance that line increases and
horizontal distance that the line and then
use the following calculation.
gradient =
vertical change
horizontal change
5. Note: A negative gradient means that the line is
travelling downhill or a decline.
6. Calculating the gradient from co-ordinates
It is possible to calculate the gradient of a line just
by knowing two co-ordinates that the line passes
through.
This can be achieved in two ways:
1. Draw the co-ordinates on a grid and use the
previous method.
Gradient = Change in y
Change in x
Vertical
horizontal
=
7. 2. Using a formula that has been specifically
generated for the calculation.
Let a line pass through two co-ordinates (X1,Y1)
and (X2,Y2).
Gradient = Change in y
Change in x
= Y2 - Y1
X2 - X1
9. Example:
Calculate the gradient of the line between the following
pairs of co-ordinates.
1. (1,2) and (5,18)
Note: The gradient of a line is more usually given
the label (m).
Y2 - Y1
X2 - X1
=
m 18 - 2
5 - 1
= = 16
4
= 4
