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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),

and the gradient of the line, m is .

Using the two point formula

y – y1 =   (x – x1)

y – b =   (x – 0)

y – b =  – x

Dividing by +b on both sides –

=

=

– 1 =  0, or

=  1

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

=  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

=  1

=  1

Multiplying each term by 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

=  1

=  1

Multiplying each term by 24 –

=  1 x 24

3x – 8y = 24

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