Slope

Question

Q)

hobbit · Answer

a is the correct answer.

mbagal1 · Answer

I get C. For line to be in the second quad, there has to be a set of x and Y for which x <0 and y >0.

We know y = mx+c

1) given: m = -1/6

y = -x/6 + c

For x < 0, -x/6 > 0, but we do not know c. -x/6 + c could be less than 0.
-x/6+c<0 for all -x + 6c < 0 or c < x/6

2) given: for x = 0, y= -6
=> -6 = 0 + c => c = -6
Again, by itself insuff, since we do not know the slope

Together,

y = -x/6 - 6 so for x < 0, there could be a set of y's which are positive when -x/6 - 6 >0
=> -x/6 > 6
=> -x > 36
=> x < -36.

mbagal1 · Answer

Oh, BTW, without the calculations, I would have thought A too, since a negative slope should mean it will go into the second quad at some point. Did I do something wrong in my calculations?

usman7 · Answer

hsmpath, the answer is a.I also came to the same answer i.e. c...but dont know why its a. 

hobbit can you please explain why you got A in the above.

Also aside from this, theres one more thing I want to ask, whenever we move the line by 90 deg, the new slope is the neg reciprocal of the previous one,....why cant it get positive...like suppose if it was negative before, why cant it get positive after moving 90 deg?how do we know thats its always going to be negative reciprocal....

mbagal1 · Answer

Ah, I get it. See where I said -x/6 + C can be less than 0 for c < x/6?

well, C is a constant and does not change based on x. so while there could well be a part of the line in the 3rd quad, it will at some point go into the 2nd quad.

usman7 · Answer

good job hsampath....got it now...thanks..

Can you also explain my other question... i.e.
"
Also aside from this, theres one more thing I want to ask, whenever we move the line by 90 deg, the new slope is the neg reciprocal of the previous one,....why cant it get positive...like suppose if it was negative before, why cant it get positive after moving 90 deg?how do we know thats its always going to be negative reciprocal...."

mbagal1 · Answer

Oh, that could be because, when we talk about 90 degrees, or any angle for that matter, its always from left to right, so no matter where the line is sloping, it will slope further to the left. 
To have what you are asking about happen, when the slope is negative, it might mean the line has to be shifted by 270 degrees.

anindyat · Answer

Going for A
any line with negative slope has to go through QII

BLISSFUL · Answer

similarly, any line with +ve slope has to go thru quadrant I.

Slope

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