(a) 4x + 3y = 24
Let the x-intercept = a. Then, y-intercept = 14 – a
∴ Eqn of the straight line is \(\frac{x}{a}\) + \(\frac{y}{14-a}\) = 1
Since it passes through (3, 4), so
\(\frac{3}{a}\) + \(\frac{4}{14-a}\) = 1
⇒ 3(14 – a) + 4a = a (14 – a)
⇒ 42 – 3a + 4a = 14a – a2
⇒ a2 – 13a + 42 = 0
⇒ (a – 7) (a – 6) = 0 ⇒ a = 7 or 6.
∴ Eqn is \(\frac{x}{7}\) + \(\frac{y}{7}\) = 1 ⇒ x + y = 7
or \(\frac{x}{6}\) + \(\frac{y}{8}\) = 1 ⇒ 8x + 6y = 48 ⇒ 4x + 3y = 24.
