Equation of Lines Parallel to Axes

(i) Equation of a Line Parallel to the X-Axis:
Consider that $$l$$ is the straight line which is passing through the point $$A\left( {0,b} \right)$$ and is parallel tothe $$X$$-axis because this point lies on the $$Y$$-axis and any point on the Y-axis whose values of $$x$$ are zero.


line-equation-parallel-axes

Then the equation of a line parallel to the X-axis is given by
\[\boxed{y = b}\]

(ii) Equation of a Line Parallel to the Y-Axis:
Consider that $$l$$ is the straight line which is passing through the point $$B\left( {a,0} \right)$$ and is parallel to the $$Y$$-axis, because this point lies on the $$X$$-axis and any point on the X-axis whose values of $$y$$ are zero.


line-equation-parallel-axes-2

Then the equation of a line parallel to the Y-axis is given by
\[\boxed{x = a}\]