In the coordinate plane system, does line L pass through 3rd quadrant?
1) The slope of line L is positive.
2) Line L has x-intercept -2 and y-intercept 3.
The OA is D.
How is statement 1 sufficient? Can someone elaborate, please? Thanks!
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In the coordinate plane system, does line L pass through
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Keith@ThePrincetonReview
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Hi swerve,swerve wrote:In the coordinate plane system, does line L pass through 3rd quadrant?
1) The slope of line L is positive.
2) Line L has x-intercept -2 and y-intercept 3.
The OA is D.
How is statement 1 sufficient? Can someone elaborate, please? Thanks!
To answer your question, consider a vertical line and a horizontal line.
Were line L to be a vertical or horizontal line, then it would be possible for line L not to pass through the 3rd quadrant (for example, consider the lines x = 2 and y = 2, neither of which passes through the 3rd quadrant).
However, the slope of a horizontal line is 0, and the slope of a vertical line is undefined, so if line L has a positive slope, then line L can't be vertical or horizontal.
Finally, because a line is of infinite length, a line with a positive slope will eventually pass through the 3rd quadrant.
Statement (1) is sufficient to produce a consistent "Yes" answer, and since Statement (2) provides the coordinates of two points on the line, it is also sufficient to produce a consistent "Yes" answer.
The correct answer is choice D.
