Explore The Slopes of lines that are parallel and Perpendicular to a given line (in red).
Click Show Parallel or Show Perpendicular to get started.
Drag the two original blue points to create a new starting line. (Drag point D to move the parallel line.)

Parallel Line: Create a few lines through two given points.
Note the slopes of the original lines, and the slopes of the Parallel Lines. (Simplification of all slopes might be necessary.)
What do you notice about the slopes?
Describe a rule to determine the slope of a parallel line to a given line.
Perpendicular lines: Create a few lines through two given points.
Note the slopes of the original lines and the slopes of the Perpendicular lines.
What do you notice about the slopes?
What number do these slopes multiply together to be?
Describe a rule to determine the slope of a perpendicular line to a given line.