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Question
Find the equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15
Solution
The equation of the given line is
2x + 3y = 10 ......(1)
The equation of any line parallel to (1) is
2x + 3y = k ......(2)
`(2x)/"k" + (3y)/"k"` = 1
`x/("k"/2) + y/("k"/3)` = 1
Given that the sum of the intercepts of the line (2) on the axes is 15
∴ `"k"/2 + "k"/3` = 15
`(3"k" + 2k")/6` = 15
5k = 90
⇒ k = `90/5`
= 18
∴ The equation of the required line is 2x + 3y = 18
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