What is (y2-y1)/(x2-x1) FOR

is it to get a perpendicular line?

or what

in the y=mx+c topic in GCSE maths

Two points on a line are ( x1 , y1 ) and ( x2 , y2 )
Gradient m is then given by :-

y2 - y1
-------------
x2 - x1

In the standard y = mx + c equation for a straight line, the formula describes the slope (m) of the line, by using two points with coordinates (x1, y2) and (x2, y2)

Slope (m) = rise / run = Δy / Δx = (y2-y1)/(x2-x1)

its to get slope :)