Step-by-step answer with explanations:
Recall that a coordinate pair such as (5,-1) has two components.
The first (5, -1) means that the point is situated at x=5.
The second (5, -1) means that the point is situated at y=-1.
Now, a horizontal line through (5,-1) means that ALL points on the line have y-coordinate equal to -1, so that any point with y=-1 will lie on this horizontal line. An example would be (-2,-1).
A vertical line through (5, -1) means that ALL points on the line have x-coordinate equal to 5, so that any point with x=5 will lie on this vertical line. An example would be (5,4).