Question 91352
First, put the equation of each line into y=mx+b form:
Line #1:
{{{x-4y=12}}}
{{{-4y=-x+12}}}
{{{highlight(y=x/4-3)}}}
Line #2:
{{{4x+y=4}}}
{{{highlight(y=-4x+4)}}}
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You can tell the relationship between the lines by looking at their slopes:
* Parallel Lines have equal slopes.
* Perpendicular Lines have slopes which are negative reciprocals of each other.
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Since you put the given lines into y=mx+b form, you can just read off the slopes of each one, which is the "m" term:
Slope of Line #1 = 1/4
Slope of Line #2 = -4
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As you can see, the slopes are negative reciprocals of each other. 
So, the lines are Perpendicular.
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Good Luck,
tutor_paul@yahoo.com