I think that the reason x= 7 is a vertical line is because it is an even number and on the number line it is a positive number and if you go the other it turns in to negative numbers. That is when it is used on the number ine.
The line given by the equation x = 7 is a vertical line since all the points on this line have the same x-value, namely 7. The y-values do, however, differ.