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