# The Point Slope Equation of a Line

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 .

From draw perpendicular to the X-axis and from point draw also perpendicular to the X-axis. Also from draw perpendicular to on .

Now from the given diagram, consider the triangle . By the definition of a slope we take

Now by the definition we can use instead of , and we get

This is the equation of a straight line having slope and passing through the point .

__NOTE__**:** There is an alternate way to prove the slope point form of the equation of a line. Let be any point on the line.

Considering the slope intercept form of the equation of a line, we have

Since the line passing through the point above equation (i) becomes

Now subtracting equation (ii) from equation (i), we get

__Example__**:** Find the equation of a straight line having the slope and passing through the point

Here we have slope and point

Now the slope point form of the equation of a straight line 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.