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Question 57486: Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 4y = 12
L2 with equation 4x + y = 4
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 4y = 12
L2 with equation 4x + y = 4
Putting equations is slope intercept form  , m=slope, (0,b)=y-intercept, makes it easy to see their slopes. Parallel lines have = slopes, perpendicular lines have slopes that are negative reciprocals (opposite signs and upside down), if they aren't either of those, it's neither.
L1) x-4y=12
-x+x-4y=-x+12
-4y=-x+12
-4y/-4=-x/-4+12/-4
y=(1/4)x-3 The slope of L1, m=1/4
L2) 4x+y=4
-4x+4x+y=-4x+4
y=-4x+4 The slope of L2 is m=-4/1
The slopes are negative reciprocals of each other, therefore the lines are perpendicular.
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