Mihail is technically correct. But, let's assume you have an "up vector" that defines what the global up/down direction is. (This might commonly be \<0, 1, 0> if you use Y-up or \<0, 0, 1> if you use Z-up.)
You already know a line is defined by a point and direction. To create another parallel line you keep the same direction and just move the point. So, to create a second line 5 units above the first, you would add 5 times your up vector to the point.