Find the equation of a straight line parallel to $2 x + 3 y + 11 = 0$ and which is such that the sum of its intercepts on the axes is $15.$

2 x + 3 y = 15

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3 x + 2 y + 11 = 0

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2 x - 3 y = 10

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2 x + 3 y = 18

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Solution

The correct option is D $2 x + 3 y = 18$
Line parallel to $2 x + 3 y + 11 = 0$ is
$2 x + 3 y + c = 0$ ---(1)
So, x-intercept $= \frac{- c}{2}$ (Put $y = 0$ )

y-intercept $= \frac{- c}{3}$ (Put $x = 0$ )

As given $(\frac{- c}{2}) + (\frac{- c}{3}) = 15$
$\frac{- 5 c}{6} = 15$
$c = - 18$

From (1),

$∴$ equation of that line is $2 x + 3 y - 18 = 0.$

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10

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