If is the incrimination of a straight line passing through the point then its equation of a straight line is
Now to prove this formula of a straight line, let be any point on the given line . Consider another point , since the line passes through the point .
Let be the inclination of the straight line as shown in the given diagram.
From draw a line which is perpendicular to the X-axis and from point draw another line which is also perpendicular to the X-axis. Also from draw a line perpendicular to .
Now from the given diagram, consider the triangle . By the definition of a slope we take
Now by using the trigonometric ratio formula as , the above form can be written as
This is called the symmetric form of an equation of a straight line having point and inclination .
Example: Find the equation of a straight line with inclination and passing through the point
Here we have inclination and point
The equation of line in its symmetric form is
Substitute the above values in the formula to get the equation of a straight line
This is the required equation of a straight line.