How do you construct parallel lines?

Parallel lines are lines that never cross each other. The key to constructing parallel lines is to know that they have the exact same slope.

1. Determine two points on a given line.

   Find two separate points in the (x,y) form on a given line. Call these two points (x1, y1) and (x2, y2).

2. Calculate the slope of the given line.

   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.

3. Plug the slope into a new line.

   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.

4. Find a new y-intercept.

   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.