Consider the straight line and let be the inclination of the straight line as shown in the given diagram. Now the slope of the line is represented by . Let be any point on the given line . Let be the X-intercept of the straight line, so the line must pass through the point .
Take as the X-intercept of the straight line so the line must pass through the point , i.e. X-intercept. From point draw perpendicular to the -axis.
Now from the given diagram, consider the triangle , i.e. , and 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 X-intercept .
NOTE: It may be noted that if the line passes through the origin , then the X-intercept is equal to zero, i.e. , so the equation of the straight line becomes .
Example: Find the equation of a straight line having the slope and X-intercept equal to.
Here we have slope and X-intercept
Now using the formula of a straight line having a slope and X-intercept
Substitute the above values in the formula to get the equation of a straight line
This is the required equation of straight line.