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parallel lines

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by nasir » Sun Sep 26, 2010 12:27 pm
Two lines A and B are parallel

Equation of line A is x= 3-4y

What would be the equation of line B ?

Please explain your answer, if possible include an example too

Thanks in advance.
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by Ian Stewart » Sun Sep 26, 2010 12:56 pm
nasir wrote:Two lines A and B are parallel

Equation of line A is x= 3-4y

What would be the equation of line B ?

Please explain your answer, if possible include an example too

Thanks in advance.
If you rewrite the equation of line A in the form y = (-1/4)x + 3/4, you can see that line A has a slope of -1/4 (when the equation of a line is written in the form y = mx + b, then m is the slope). Parallel lines have the same slope, so the equation of a parallel line will look like y = (-1/4)x + c, where c is some number. There are a lot of different lines which are parallel to A, so we can't produce an exact equation here without more information.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by tlt2372 » Sun Sep 26, 2010 1:01 pm
Re-arrange the equation to slope intercept form..

y=-1/4(x)+3/4

The slope of a line parallel to line A has the same slope as line A. So the slope of Line B will be -1/4.

You can use the point slope formula to calculate the equation for Line B. Pick a point that you want Line B to go through.

I chose (0,0)

So y-y1 =m(x-x1) where y1 and x1 are (0,0)

Solving you get y=-1/4x+0
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by nasir » Sun Sep 26, 2010 1:38 pm
Parallel lines have the same slope
it means, there is only one condition for lines to be parallel and that is " same slope ". In
y=mx+b What about b ? is it necessary for parallel lines to have different values of b or b
could be same as well ?

Thanks
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by tlt2372 » Sun Sep 26, 2010 2:51 pm
nasir wrote:
Parallel lines have the same slope
it means, there is only one condition for lines to be parallel and that is " same slope ". In
y=mx+b What about b ? is it necessary for parallel lines to have different values of b or b
could be same as well ?

Thanks
If you have the same slope, represented by m in the slope intercept equation, and the same b, the lines would be on top of one another.

Ian was right when he said to completely solve this problem, you need a coordinate. I chose (0,0) because it was easy to work with. If you were given a question on the gmat, they would give you another coordinate since there are endless possibilities without one.

Hope this helps
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by nasir » Sun Sep 26, 2010 5:33 pm
I got what i was looking for

Thanks Tlt and Ian
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