Once you know the equation of a line, there is a variety of questions you can ask. One of the easiest to as is, "What points are on the line?" The points on the line can be found by plugging in one coordinate and solving for the other. For example, if the line equation is y=3x+1, and you want to see what point with an x coordinate of 1 is on the line then you would plug in 1, and the equation would be 3(1)+1=y, or y=4. Another question that can be asked is, "What points are NOT on the line?" This can be determined by plugging in both coordinates, and seeing if the equation is true. For example, if you wanted to know if the point 1, 5 is on the previously said line or not, you would rewrite the equation to look like this: 5=3(1)+1. When you simplify the equation, you get 5=4, which is not true. 

You can also find out which lines are parallel to the given line. Parallel lines have the same slope. For example, if you had the lines y=3x+1 and y=6/2x+8, you could simplify the latter to get y=3x+1 and y=3x+8. In parallel lines, it does not matter what the constants are as long as the slopes are the same.