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30 Aug 2018, 05:03
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A
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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
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
30 Aug 2018, 05:47
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Bunuel
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
Cheers,
Brent
30 Aug 2018, 19:57
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Bunuel
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
