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