What is the equation of the straight line which passes through (3, 4) and the sum of whose x-intercept and y-intercept is 14 ? -Maths 9th

What is the equation of the straight line which passes through (3, 4) and the sum of whose x-intercept and y-intercept is 14 ? -Maths 9th
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1 Answer

Answer :

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