SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 2y = 10 L2 with equation 2x + y = 2

Algebra ->  Points-lines-and-rays -> SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 2y = 10 L2 with equation 2x + y = 2       Log On


   

Question 108605: Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 2y = 10
L2 with equation 2x + y = 2
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
L1 :x-2y=10
L2 :2x+%2B+y+=+2
Re-arrange your equations into the slope-interept form.
L1 :x-2y=10
L1 :-2y=10-x
L1 :y=x%2F2-5
L2 :2x%2By=2
L2 :y=-2x%2B2
Slope of L1 is m%5B1%5D=1%2F2.
Slope of L2 is m%5B2%5D=-2.
Parallel lines have equal slopes.
m%5B1%5D=m%5B2%5D
Perpendicular lines have slope that are negative reciprocals.
m%5B1%5D=%28-1%29%2Fm%5B2%5D
Since
1%2F2=%28-1%29%2F%28-2%29
L1 and L2 are perpendicular.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Put the equations into slope-intercept form.
--------------
Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 2y = 10
2y= x-10
y = (1/2)x-4
slope = 1/2
----------------
L2 with equation 2x + y = 2
y = -2x+2
slope = -2
----------------
Product of the slopes = (1/2)*-2 = -1
so the lines are perpendicular.
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Cheers,
Stan H.