Let and be any two points on the given line . Also consider be the inclination of the line as shown in the given diagram. From point draw perpendicular on X-axis also from draw perpendicular on X-axis.
Now from the given diagram, consider the triangle , from the definition of slope we take
Now by definition we can use instead of , we get slope of a line through two points is
Example: Find the slope of straight line passing through the pair of points and .
Here we have two points suppose that and now using the formula of slope passing through two given points of the straight line
Substitute the above points in the formula we the slope of line as
Here is the required slope of the line.