Positive and negative gradients
The slope of a line can be 'seen' to be sloping uphill or to be sloping downhill.
The examples so far have been sloping uphill as you look at the diagrams from left to right.
When a line is sloping uphill from left to right the gradient is given a positive value.
When a line is sloping downhill from left to right the gradient is given a negative value.
Example
\(gradient\,of\,line\,EF = \frac{{vertical\,height}}{{horizontal\,distance}}\)
\(vertical\,height = 4\,m\)
\(horizontal\,distance = 10\,m\)
\(gradient = \frac{4}{{10}} = \frac{2}{5}\)
The line is sloping downhill. Therefore the gradient has a negative value.
\(gradient\,of\,line\,EF = - \frac{2}{5}\)
Horizontal lines have a gradient that is zero, ie they are not sloping uphill or downhill.
Vertical lines have a gradient that we say is 'undefined', ie we are unable to give them a numerical value.
