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If the slope of l2 is equal to that of a different line, l1, which of

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If the slope of l2 is equal to that of a different line, l1, which of  [#permalink]

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New post 30 Aug 2018, 04:03
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

56% (00:46) correct 44% (00:47) wrong based on 63 sessions

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If the slope of l2 is equal to that of a different line, l1, which of the following could be true?

I. l1 and l2 have the same x-intercept.
II. l1 and l2 have the same y-intercept.
III. l1 and l2 have exactly 1 point in common.


A. None
B. II only
C. III only
D. I and II only
E. I, II and III

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Re: If the slope of l2 is equal to that of a different line, l1, which of  [#permalink]

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New post 30 Aug 2018, 04:47
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Bunuel wrote:
If the slope of l2 is equal to that of a different line, l1, which of the following could be true?

I. l1 and l2 have the same x-intercept.
II. l1 and l2 have the same y-intercept.
III. l1 and l2 have exactly 1 point in common.


A. None
B. II only
C. III only
D. I and II only
E. I, II and III


If line1 and line2 have the same slope, the two lines are parallel to one another.
Also, it's POSSIBLE that the two lines are identical. HOWEVER, the question tells us that the lines are DIFFERENT.
So, we have two lines that are PARALLEL but different

If two lines that are PARALLEL but different, then they can never have the same x-intercept, or the same y-intercept.
They can't have any points in common either.

Answer: A

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Brent
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If the slope of l2 is equal to that of a different line, l1, which of  [#permalink]

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New post 30 Aug 2018, 18:57
Bunuel wrote:
If the slope of l2 is equal to that of a different line, l1, which of the following could be true?

I. l1 and l2 have the same x-intercept.
II. l1 and l2 have the same y-intercept.
III. l1 and l2 have exactly 1 point in common.


A. None
B. II only
C. III only
D. I and II only
E. I, II and III

Lines with the same slope are parallel.
The lines are different (if they were the same line, could share an x-intercept, see below)

Parallel lines never intersect. Never touch.
Parallel lines have no points in common.
Another fact: Parallel lines have identical slopes and different y-intercepts.

III. l1 and l2 have exactly 1 point in common.

Parallel lines have NO points in common
-- Eliminate III
-- Eliminate options C and E

Realize that I and II are ...
Impermissible points in common.

I. Share an x-intercept:
-- that intercept point would be (x,0) -- for BOTH lines.
-- Incorrect. Parallel lines have no points in common.
To share an x-intercept is to share a point, to have that point in common.

Eliminate D

II. Share a y-intercept.
-- That point would be (0,y) -- for BOTH lines.
-- Incorrect. Parallel lines have no points in common
To share a y-intercept is to share a point, to have that point in common.

Eliminate B

ANSWER A
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If the slope of l2 is equal to that of a different line, l1, which of &nbs [#permalink] 30 Aug 2018, 18:57
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