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Intercept Form of a Straight Line

The intercept form of a straight line involves finding the equation of the straight line that cuts off intercepts a and b on the x and y axes respectively.

Here, the line passes through the two points (a, 0) and (0, b), intercept_form

and the gradient of the line, m is b/a.

Using the two point formula

y – y1 =  ({y_2~-~y_1}/{x_2~-~x_1}) (x – x1)

y – b =  ({0~-~b}/{a~-~0}) (x – 0)

y – b =  –b/a x

Dividing by +b on both sides –

y/{+b}~-~b/{+b}  =  {-bx}/{+ba}

y/b~-~1  =  {-x}/a

x/a~+~y/b – 1 =  0, or

x/a~+~y/b  =  1

The equation of a straight line cutting off intercepts a and b on the x and y axes respectively is –

 x/a~+~y/b  =  1

 

Example 1 : Find the equation of the straight line making x-intercept of 6 and y-intercept of 3. Express this equation in general form also.

x-intercept = a = 6

y-intercept = b = 3

Equation of a straight line is

x/a~+~y/b  =  1

x/6~+~y/3  =  1

Multiplying each term by 6 –

{x/6}*6~+~{y/3}*6  =  1 x 6

x + 2y = 6.

This equation in general form will be x + 2y – 6 = 0

 

Example 2 : Find the equation of the straight line making x-intercept of 8 and y-intercept of -3. Express this equation in general form also.

x-intercept = a = 8

y-intercept = b = -3

Equation of a straight line is

x/a~+~y/b  =  1

x/8~+~y/{-3}  =  1

Multiplying each term by 24 –

{x/8}*24~+~{y/{-3}}*24  =  1 x 24

3x – 8y = 24

This equation in general form will be 3x – 8y – 24 = 0