Find two separate points in the (x,y) form on a given line. Call these two points (x1, y1) and (x2, y2).
Using the two points previously found, calculate the slope of the given line using the formula (x1 - x2) / (y1 - y2). Simplify the result as much as possible. For example, 4/2 should be simplified to 2.
To construct a parallel line, a new line must be derived that has the exact same slope as the given line. Start by writing the standard form for a line, y = mx + b. Plug the calculated slope in as the value of m.
Look at the graph of the given line and see where it intersects the y-axis. This point is called the y-intercept. To construct a parallel line, a different y-intercept must be chosen. This new value is plugged into the y = mx + b formula as the b-value, giving you the formula for a new line parallel to the original.