SOLUTION: Parallel and Perpendicular Slope Please help me solve this equation: Which lines are parallel? a.x=7 b.y=5/6x+8 c.y=5/6x-4 d.x=9

Algebra ->  Linear-equations -> SOLUTION: Parallel and Perpendicular Slope Please help me solve this equation: Which lines are parallel? a.x=7 b.y=5/6x+8 c.y=5/6x-4 d.x=9      Log On


   

Question 208435: Parallel and Perpendicular Slope
Please help me solve this equation: Which lines are parallel?
a.x=7
b.y=5/6x+8
c.y=5/6x-4
d.x=9
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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if the slopes are the same, then the lines are parallel.
if the slopes are negative reciprocals of each other than the lines are perpendicular.
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your choices are:
a.x=7
b.y=5/6x+8
c.y=5/6x-4
d.x=9
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b and c are parallel to each other because they have the same slope.
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a and d are parallel to each other because they are both perpendicular to the x axis at that point and are therefore parallel to each other.
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first b and c.
graph is of y = 5/6x + 8 and y = 5/6x -4
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graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%285%2F6%29x+%2B+8%2C+%285%2F6%29x+-+4%29
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next a and c.
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i can't draw them directly on algebra.com but i can fudge the normal equation to make them look vertical, or almost vertical.
doing that, they will look like this.
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graph%28300%2C300%2C-1%2C10%2C-10%2C10%2C1000000%2F%28x-7%29%2C1000000%2F%28x-9%29%29
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you can see that both lines are perpendicular to the x-axis and therefore parallel to each other.
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having the same slope was easy to show mathematically with b and c.
showing that a and d have the same slope is a lot harder.
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trust me, they are.
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the problem stems from the fact that their slope is equal to infinity which is not a real number because it's undefined.
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nevertheless, both their slopes are equal to infinity so i would say they are equal to each other even though there are people who would argue otherwise. can one infinity really be larger than another?
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since both these lines are perpendicular to the x-axis, which is a fact not in dispute as far as i known, then both their slopes are negative reciprocals of 0 which should also strengthen the argument that their slopes are equal.
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bottom line is they threw you a wrinkle when they gave you the equations of x = 7 and x = 9.
these lines are clearly parallel to each other but proving it leads into the murky world of infinity which has stumped smarter persons than me.
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