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Are the lines parallel?

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by gmattesttaker2 » Sun Nov 24, 2013 2:25 pm
Hello,

For this problem:

In a rectangular coordinate system, a, b, and c are non-zero integers, ab < 0, and c < 0. Is line
ax - by - c = 0 parallel to line 4x - 2y - 3 = 0?

1) c = - 4b
2) a = 2b

OA: B

can you please tell me when will 2 lines be parallel (and also perpendicular)?

I attempted to solve as follows:

ax - by - c = 0
=> -by = -ax + c
=> by = ax - c
=> y = (a/b)x - (c/b)

So, m = (a/b)

4x - 2y - 3 = 0
=> -2y = -4x + 3
=> 2y = 4x - 3
=> y = 2x - (3/2)

So, m = 2

However, I could not proceed from here. Can you please assist? Thanks - Sri
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Source: — Data Sufficiency |

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by [email protected] » Sun Nov 24, 2013 6:39 pm
Hi Sri,

You were remarkably close to solving this question. Here's how:

Two lines are parallel if they have the SAME SLOPE.

By manipulating the second line equation, you determined that it's SLOPE = 2. So this DS question is really asking if the slope of the first line = 2?

You manipulated the first equation and got it to this:

y = (a/b)x - (c/b)

Fact 2: a = 2b

Substitute in THAT value and watch what happens:

y = (2b/b)x - (c/b)

y = 2x - (c/b)

Now you have proof that the slope DOES = 2, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

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by gmattesttaker2 » Sun Nov 24, 2013 9:14 pm
[email protected] wrote:Hi Sri,

You were remarkably close to solving this question. Here's how:

Two lines are parallel if they have the SAME SLOPE.

By manipulating the second line equation, you determined that it's SLOPE = 2. So this DS question is really asking if the slope of the first line = 2?

You manipulated the first equation and got it to this:

y = (a/b)x - (c/b)

Fact 2: a = 2b

Substitute in THAT value and watch what happens:

y = (2b/b)x - (c/b)

y = 2x - (c/b)

Now you have proof that the slope DOES = 2, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
Hi Rich,

Thanks for the detailed explanation. I recall reading somewhere that 2 lines are perpendicular if the product of their slopes is -1. Is this correct?

Thanks,
Sri
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by [email protected] » Mon Nov 25, 2013 2:48 pm
Hi Sri,

Yes, that's one way to prove that two lines are perpendicular.

From a "visual" standpoint, two lines are perpendicular if they have "opposite, inverse" slopes.

For example, if we have a line with a slope of 2, a line that is perpendicular to that line will have a slope of -1/2 (negative is the opposite of positive; 1/2 is the inverse of 2).

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