Question

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

Answer 1

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 $x=2.$