If and are non-zero and intercepts of a line , then its equation is of the form
Since is an -intercept of the line , and as we know that if any point lies on the -axis its value of is equal to zero, it passes through the point . Also if is the -intercept of the line , and we know that any point that lies on the -axis has a value of equal to zero, it passes through the point as shown in the given diagram.
Now to prove the intercepts form of a line, use the formula for the two points form of a straight line as given by
Take and , and put these values in the above formula:
This is the required equation of a straight line in intercepts form.
Example: Find the equation of a straight line with -intercept and -intercept .
From the above information we know the -intercept is and the -intercept is . Now we put all these values in the formula of the intercepts form as given:
This is the required equation of a straight line.