Consider the straight line . Let be any point on the given line . Suppose that be the inclination of the line as shown in the given diagram, i.e.
Take as a -intercept of the straight line because it cutting the -axis at the point , i.e. -intercept.
From point draw perpendicular on -axis also from draw perpendicular on .
Now from the given diagram, consider the triangle , i.e. , 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 Y-intercept .
NOTE: It may be noted that if the line passes through the origin , then take -intercept is equal to zero i.e. , so the equation of straight line becomes .
Example: Find the equation of straight line having slope and -intercept is equal to 8.
Here we have slope and -intercept
Now using the formula of straight line having slope and -intercept
Substitute the above values in the formula to get the equation of straight line
Which is the required equation of straight line.