Question

1.) What is the equation of a vertical line passing through the point (2, -4)?

Answer 1

The points lying on a vertical line share the same $x$ coordinate. Similarly, the points lying on a horizontal line share the same $y$ coordinate.

So, vertical lines are identified by the $x$ coordinate of their points, and have an equation like $x=x_0$, where $x_0$ is a fixed real number.

Similarly, horizontal lines are identified by the $y$ coordinate of their points, and have an equation like $y=y_0$, where $y_0$ is a fixed real number.

We are ready to answer the questions:

1. A vertical line passing through the point (2, -4) has equation $x=2$
2. A horizontal line passing through the point (2, -4) has equation $y=-4$
3. The two lines are perpendicular