Equation of a line in intercept form is
\(\frac{x}{a}+\frac{y}{b}=1\)
Given, a + b = 1
and a × b = – 6
⇒ a −\(\frac{6}{a}\) = 1
⇒ a2 − a − 6 = 0
⇒ (a − 3) (a + 2) = 0
⇒ a = 3, – 2.
If a = 3, b = – 2 and if a = – 2, b = 3.
∴ Equation of the line is
\(\frac{x}{3}-\frac{y}{2}=1\) or \(\frac{x}{-2}-\frac{y}{3}=1\)
⇒ 2x – 3y – 6 = 0 or 3x – 2y + 6 = 0,
is the required equation of the line