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# EQUATION OF A LINE IN INTERCEPT FORM

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The equation of a line which cuts off the given intercept on both the coordinate axes is determined as follows:

Let PQ be a line meeting x-axis in A and y-axis in B.

Consider OA = a, and OB = b.

Then, the coordinates of A and B is .

The equation of line joining A and B is written as follows: Therefore, the equation a straight line in a intercept form is written as .

Example

The equation of a line which cuts off the intercepts 5 and -3 on x and y axes.

The general equation of straight line in intercept form is Given that a = 5 and b = – 3

Substitute the value as follows: Therefore, the required equation is .

Question 1

Find the equation of a line which cuts off the intercepts 10 and 2 on x and y axes.

Solution 1

The general equation of straight line in intercept form is Given, a = 10 and b = 2

Substitute the value as follows: Therefore, the required equation is .

Question 2

Find the intercepts made by the line on the coordinate axes.

Solution 2

The general equation of straight line in intercept form is Consider the line and rewrite the equation as follows: Divide both the sides of the equation by –12 as follows: Therefore, the intercept on the axes are –4 and 6 respectively.

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