Suppose the intercepts be a and b
Given : Sum of intercepts = 1 i.e. a + b = 1 ... (i)
and product of intercepts = – 6 i.e. ab = – 6 ... (ii)
From (i) & (ii), we get
a(1 – a) = – 6 ⇒ a2 – a – 6 = 0 ⇒ a = 3, –2.
Case (I) : If a = 3, then b = −

6

a

= −

6

3

= - 2
∴ Equation of the line is

x

3

+

y

−2

[Since x/a +y/b = 1]
⇒ – 2x + 3y = – 6 ⇒ 2x – 3y – 6 = 0
Case (II) : If a = – 2, then b = −

6

a

= −

6

−2

= 3
Thus equation of the line is

x

−2

+

y

3

= 1
⇒ 3x – 2y = – 6 ⇒ 3x – 2y + 6 = 0.