Let be the inclination of the straight line as shown in the given diagram. Let be any point on the given line . Consider another point , since the line passes through the point .
Form draw perpendicular on X-axis and from point draw also perpendicular on X-axis. Also from draw perpendicular on .
Now from the given diagram, consider the triangle , by the definition of slope we take
Now by definition we can use instead of , we get
Which is the equation of straight line having slope and passing through the point .
NOTE: There is an alternate way to prove slope point form of equation of a line. Let be any point on the line.
Consider the slope intercept form of equation of a line, we have
Since the line passing through the point , above equation (i) becomes
Now subtraction equation (ii) form equation (i), we get
Example: Find the equation of straight line having slope and passing through the point
Here we have slope and point
Now slope point form equation straight line
Substitute the above values in the formula to get the equation of straight line
Which is the required equation of straight line.