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Slope of the line

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Slope of the line

by Mayur Sand » Wed Jul 22, 2009 8:52 am
In the xy-plane, what is the slope of line l?
(1) Line l dose not intersect the line with equation y = 1 - x.
(2) Line l intersects the line with equation y = x – 1.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA A
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Re: Slope of the line

by El Cucu » Wed Jul 22, 2009 10:01 am
Mayur Sand wrote:In the xy-plane, what is the slope of line l?
(1) Line l dose not intersect the line with equation y = 1 - x.
(2) Line l intersects the line with equation y = x – 1.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA A
1) If line I does not intersect a line with points 1,1 and with negative slope, we know that line I should be parallel to the line that does not intersect, so Line I has the same slope than that line.

2) If line I intersects the line y=x-1 which passes through points 1,-1, line I could intersect that line form different angles so we can´t know for sure the slope of line I.
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by Mayur Sand » Wed Jul 22, 2009 11:07 am
Hi thanks for reply , you mind explaining point 1 again , i didnt the complete crux
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by jjk » Wed Jul 22, 2009 11:51 am
The basic rules of slopes in coordinate geometry are:

- If the slopes of the lines are NOT equal, they intersect at one point somewhere on the xy plane.

- If the slopes of the lines are equal, the lines are parallel and can thus NEVER intersect.

- If the equations representing the lines are equal, the lines are essentially the same line and have an infinite number of solutions (intersections).
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