Parallel and Perpendicular Lines
Date: 01/14/99 at 20:51:19 From: Anonymous Subject: Algebra: linear equations How do you tell if the graphs of these equations are parallel, perpendicular, or neither without graphing? 4y - 5 = 3x + 1 and 12 = -6x + 8y - 3
Date: 01/15/99 at 15:47:54 From: Doctor Teeple Subject: Re: Algebra: linear equations Hello, Thanks for writing to Dr. Math. The best way to get information on how two lines relate to each other (i.e.: if they are parallel, perpendicular, or neither) is to look at their slopes. And the easiest way to find the slopes is to get your equations into slope intercept form, which means they look like this: y = m x + b Then we can read the slope right off the equation: it is the number represented by m. I'll help you get one into this form: Start with 4y - 5 = 3x + 1. Then add 5 to both sides: 4y = 3x + 6. Then divide both sides by 4: y = 3/4 x + 6/4. This means that the slope is 3/4. Try the other one on your own and reduce the slope to the smallest possible fraction. Now, what does this mean? If the slopes are the same, it means the two lines are parallel. If one slope is the negative reciprocal of the other, then the two lines are perpendicular. To get the negative reciprocal of a number, put one over the number and then make it negative. So: if the number is its negative reciprocal is 2 -1/2 3/10 -10/3 -3/2 2/3 So if the two lines had these respective slopes, they would be perpendicular. If the slopes are neither the same nor negative reciprocals, the lines are neither parallel nor perpendicular. If you need more about putting equations in slope intercept form or on parallel and perpendicular lines, try searching the archives. For example, I found: Using the Slope-Intercept Formula http://mathforum.org/dr.math/problems/plotkin27.html Perpendicular/Parallel Lines http://mathforum.org/dr.math/problems/hartge1.17.97.html If you need more help with these ideas, please write back. - Doctor Teeple, The Math Forum http://mathforum.org/dr.math/
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