To create a parallel line from a given line, we start by identifying the slope of the original line. Then we write a second equation, repeating the slope but changing the y-intercept. Once again, because there are an infinite number of possible y-intercepts, there are an infinite number of equations we could create. Spend a few moments adjusting the blue line on the graph in the interactive below, and see if you can make it parallel to the red line. The slider bar marked slope will let you manipulate the slope. First, figure out the slope of the blue line, then change the value of the slope of the blue line to be the same. When the lines are parallel the text that says "Not Parallel" will switch to "Parallel!". Now try changing the value of b, which is the y-intercept of the red line. Do you see that there are an infinite number of perpendicular lines? It doesn't matter what the y-intercepts are, lines are perpendicular as long their slopes are opposite reciprocals of one another. When you have successfully created a parallel line, click the New Line button to try again with a different line. Try to successfully create 3-5 parallel lines before you move on.
This applet created for use in Algebra 1 at Michigan Virtual School. [url]http://www.mivhs.org/[/url]