Graphing Parallel and Perpendicular Lines（图形平行和垂直的线）.pdfVIP

2.5 Graphing - Parallel and Perpendicular Lines Objective: Identify the equation of a line given a parallel or perpendic- ular line. There is an interesting connection between the slope of lines that are parallel and the slope of lines that are perpendicular (meet at a right angle). This is shown in the following example. Example 1. The above graph has two parallel The above graph has two perpendic- lines. The slope of the top line is ular lines. The slope of the flatter line down 2, run 3, or − 2 . The slope of is up 2, run 3 or 3 2 the bottom line is down 2, run 3 as 3 . The slope of the steeper line is down 3, 2 3 well, or − 3 . run 2 or − 2 . World View Note: Greek Mathematician Euclid lived around 300 BC and pub- lished a book titled, The Elements. In it is the famous parallel postulate which mathematicians have tried for years to drop from the list of postulates. The attempts have failed, yet all the work done has developed new types of geome- tries! As the above graphs illustrate, parallel lines have the same slope and perpendic- ular lines have opposite (one positive, one negative) reciprocal (flipped fraction) slopes. We can use these properties to make conclusions about parallel and per- pendicular lines. Example 2. Find the slope of a line parallel to 5y − 2x = 7. 5y − 2x =7 To find the slope we will put equation in slope − intercept form +2x + 2x Add 2x to both sides 1 5y = 2x +7 Put x term first 5 5 5 Divide each term by 5 2 7 y = x +