Investigating Parallel and Perpendicular Lines
[list][*]Take a moment and explore the relationship between the slopes, the graph, and parallel lines.[br][/*][*]Using the sliders for the [color=#ff00ff][i]slope[/i][/color] and [color=#ff00ff][i]y-intercept[/i][/color], investigate the effects of increasing and decreasing the slope of the pink line on the graph of the line.[br][/*][/list][list][*][i]Check[/i] [i]the[/i] "[b]Parallel Line[/b]" and "[b]Parallel Line Slope[/b]" [i]boxes[/i] and repeat steps A and B with the parallel lines.[/*][*]Answer the questions below regarding your exploration findings.[/*][/list][br][br]1. How does changing the slope of the pink line affect the slope of the blue parallel line?[br]2. What effect does changing the slope of the pink line have on the equation of the pink line? [br]3. How does changing the slope of the pink line affect the equation of the blue parallel line?[br]
[i]Check the [/i][b]perpendicular line[/b][i] box [/i]and the [b]perpendicular line slope[/b][i] box, [/i]then:[br][br]Use the slider, investigate the effects of increasing and decreasing the [color=#ff00ff]slope[/color] of the pink line on the slope of the perpendicular line. ([b][i]Hint: try multiplying the slopes of both lines each time you change the slope of the pink line[/i][/b])[br][br]Consider the effect these changes have on the equations of the perpendicular lines when answering the questions below.[br][br]5. How does changing the slope of the pink line affect the slope of the blue perpendicular line?[br]6. How does changing the slope of the pink line affect the equation of the blue line?[br][br]
4. Which of the following is a generalization of the relationships between the slopes of parallel lines.
[b]7. What generalizations can you make regarding the slopes of any set of all perpendicular lines?[/b][br][i](Hint: What happens when you multiply their slopes?)[/i]