The equation of a line with y-intercept $4$ and parallel to $x + 2 y + 3 = 0$

2 x + y = 8

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x + 2 y = 0

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x + 2 y = - 8

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x + 2 y = 8

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Solution

The correct option is D $x + 2 y = 8$
The equation of a line parallel to $x + 2 y + 3 = 0$ is $x + 2 y + k = 0$ ----eq.1
Now this line intercept -y axis at 4.
Therefore the coordinate is (0,4).
According to the question this point satisfies eq.1
$∴ 0 + 8 + k = 0 \Rightarrow K = - 8$
$∴$ The equation of the line is
$x + 2 y - 8 = 0 \Rightarrow x + 2 y = 8$
$∴$ option D is correct.

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