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