Let the x-intercept = a. Then y-intercept = –1 – a
The equation of the required line is \(\frac{x}{a}\) + \(\frac{y}{-1-a}\) = 1
Given, it passes through (4, 3), so,
\(\frac{4}{a}\) + \(\frac{3}{-1-a}\) = 1
⇒ – 4 – 4a + 3a = – a – a2
⇒ a2 – 4 = 0
⇒ (a + 2) (a – 2) = 0
⇒ a = –2, or 2.
When a = 2, required line is \(\frac{x}{2}\) - \(\frac{y}{3}\) = 1
When a = –2, required line is \(\frac{x}{-2}\) + \(\frac{y}{3}\) = 1