Slope definition clarification

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vidhya16: Master | Next Rank: 500 Posts; Posts: 115; Joined: Thu Mar 24, 2011 3:49 am; Thanked: 1 times

by vidhya16 » Sun Jan 08, 2012 10:41 am

1. If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.
Guys,

Im comfused with the possible values for x and y intercept as stated in the above definition. I think definition of the values are interchanged. Please can any one confirm?

Vidhya

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Source: Beat The GMAT — Data Sufficiency | Sun Jan 08, 2012 10:41 am

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sun Jan 08, 2012 2:17 pm

these definitions are good and precise

let me hint about slopes in general, as i guess their *abstract* book definition doesn't stick in memory and difficult to apply

for any line stretching from the upper left corner to the lower right the slope is negative. You'll find their relevant intercepts just by imagining these lines

for any line stretching from the upper right to the lower left the slope is positive along with the relevant intercepts defined

so, many lines defined this way can be parallel to each other. In the definition you put in post, there is condition when some parallel lines with positive and negative slopes are shifted to left or right sides (they are parallel, have the same sign of slopes, but different intercepts)

does this clear your doubt?

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vidhya16: Master | Next Rank: 500 Posts; Posts: 115; Joined: Thu Mar 24, 2011 3:49 am; Thanked: 1 times

by vidhya16 » Sun Jan 08, 2012 2:51 pm

Hi there,

So 1st and 3rd quadrant are reflection to each other. Is this what you are trying to say?

Vidhya

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sun Jan 08, 2012 3:31 pm

forget quadrants

sorry
don't think about cartesian coordinate system and set aside all your prep book notes for a moment, think about free lines in the space directed as shown in the pic
red line (solid) is one taught in your formal books for GMAT and the other thin red lines are the same slope-lines (even value the same not talking about sign). Although they may not be parallel but directed as indicated in the previous post

think about slopes as line in that direction: red is +ve and blue is -ve

it's easy to estimate x and y-intercepts then. Intercepts are where the lines cross x or y abscess

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vidhya16: Master | Next Rank: 500 Posts; Posts: 115; Joined: Thu Mar 24, 2011 3:49 am; Thanked: 1 times

by vidhya16 » Mon Jan 09, 2012 4:29 am

PEMDAS ,

Thanks you very much for your effort to make me understand the concept. But im still confused. Here is my question.

I hope I get this correct.

Postive slope line - Upper right to lower left

Negative slope line - Upper left to lower right.

I also understood the thin lines that are parallel to solid lines in your diagram . My question is how come red is +ve and blue is -ve. Line - cordinates subject is throwing me off balance. Please forgive me for the stupid questions.

Vidhya

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Jan 09, 2012 5:17 am

vidhya16 wrote:PEMDAS ,
Thanks you very much for your effort to make me understand the concept. But im still confused. Here is my question. I hope I get this correct.

Postive slope line - Upper right to lower left
Negative slope line - Upper left to lower right.

I also understood the thin lines that are parallel to solid lines in your diagram . My question is how come red is +ve and blue is -ve. Line - cordinates subject is throwing me off balance. Please forgive me for the stupid questions.

Vidhya

Try this, I am sure it will help you understand better: https://www.mathopenref.com/coordslope.html

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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vidhya16: Master | Next Rank: 500 Posts; Posts: 115; Joined: Thu Mar 24, 2011 3:49 am; Thanked: 1 times

by vidhya16 » Mon Jan 09, 2012 11:29 am

Neelagandam,

The link you gave cleared all my doubts.. Thanks a ton. PEMDAS thanks very much for your effort.

Vidhya

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