Find the equation of the line passing through the point $(2, 3)$ & making intercept of length $2$ units between the lines $y + 2 x = 3$ & $y + 2 x = 5$ .

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Solution

Both the given lines are parallel to each other.
The y-intercept of the first line $= 3$
And the y-intercept of the second line $= 5$ .
Hence the length of the part of the y-axis that is cut off by both these lines is $5 - 3 = 2.$
Hence, any line parallel to the y-axis cuts off an intercept of length 2 between both these lines.
The line passes through $(2, 3)$ .
Hence a line parallel to the y axis that passes through $(2, 3)$ is $x = 2$ .
The equation of the line is $x = 2.$

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