Question

Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1

Answer 1

Let a and b be the x and y-intercepts of the line.

Given a + b = 1

b = 1 – a  ......(1)

The equation of the straight line is

`x/"a" + y/"b"` = 1

By equation (1)

The line passes through the point (8, 3)

∴ `8/"a" + 3/(1 - "a")` = 1

`(8(1 - "a") + 3"a")/("a"(1 - "a"))` = 1

8(1 – a) + 3a = a(1 – a)

8 – 8a + 3a = a – a²

a² – 5a + 8 – a = 0

a² – 6a + 8 = 0

a² – 4a – 2a + 8 = 0

a(a – 4) – 2(a – 4) = 0

(a – 4)(a – 2) = 0

a = 4 or a = 2

When a = 2, b = 1 – 2 = – 1

When a = 4, b = 1 – 4 = – 3

∴ The equation of the straight lines are

x – 2y = 2 and 3x – 4y = 12