SOLUTION: Without graphing, determine whether the following pairs of lines are (a)parallel, (b) perpendicular, or (c) neither parallel nor perpendicular. 5x-6y=19 6x+5y=-30

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Without graphing, determine whether the following pairs of lines are (a)parallel, (b) perpendicular, or (c) neither parallel nor perpendicular. 5x-6y=19 6x+5y=-30       Log On


   

Question 536509: Without graphing, determine whether the following pairs of lines are (a)parallel, (b) perpendicular, or (c) neither parallel nor perpendicular.
5x-6y=19
6x+5y=-30
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Are they parallel, perpendicular, or neither?
1) 5x-6y+=+19 and...
2) 6x%2B5y+=+-30
First, put both equations in the "slope-intercept" form: y+=+mx%2Bb
5x-6y+=+19 Add 6y to both sides.
5x+=+6y%2B19 Now subtract 19 from both sides.
5x-19+=+6y Finally, divide both sides by 6.
%285%2F6%29x-19%2F6+=+y or
y+=+highlight%28%285%2F6%29%29x-19%2F6
Similarly for equation 2)
6x%2B5y+=+-30 Subtract 6x from both sides.
5y+=+-6x-30 Now divide both sides by 5.
y+=+highlight_green%28%28-6%2F5%29%29x-6
Compare with the "slope-intercept" form:
y+=+mx%2Bb where m is the slope.
m%5B1%5D+=+5%2F6 and...
m%5B2%5D+=+%28-6%2F5%29
You'll notice that the slopes are negative reciprocals of each other!
If two lines are perpendicular, their slopes are the negative reciprocal of each other.
What's your conclusion?