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Line k is defined by the equation ax + by = c. If the slope of line k

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Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post 17 Jan 2019, 01:47
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Line k is defined by the equation ax + by = c. If the slope of line k is positive, which of the following must be true?


A. a/b > 0

B. a/b < 0

C. a > 0

D. b > 0

E. a + b > 0

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Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post Updated on: 20 Jan 2019, 04:54
1
Bunuel wrote:
Line k is defined by the equation ax + by = c. If the slope of line k is positive, which of the following must be true?


A. a/b > 0

B. a/b < 0

C. a > 0

D. b > 0

E. a + b > 0

y=mx+c
given
ax+by=c
or say
ax-c=-by
y=- a/b x+c/b
-Y=a/bx-c/b
a/b <0
IMO B
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Originally posted by Archit3110 on 17 Jan 2019, 06:16.
Last edited by Archit3110 on 20 Jan 2019, 04:54, edited 3 times in total.
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Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post 18 Jan 2019, 04:51
Got confused

Archit3110
Can you explain this part?


ax+by=c
or say
ax-c=by

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Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post 18 Jan 2019, 05:05
1
LevanKhukhunashvili wrote:
Got confused

Archit3110
Can you explain this part?


ax+by=c
or say
ax-c=by

Regards
L

LevanKhukhunashvili

Solution attached

Posted from my mobile device
Attachments

File comment: Attached
IMG_20190118_183326967.jpg
IMG_20190118_183326967.jpg [ 3.49 MiB | Viewed 530 times ]


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Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post 20 Jan 2019, 00:28
1
Archit3110

Shouldn't it be:

ax + by = c

by = -ax + c

y = -(a/b)x + c

?
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Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post Updated on: 20 Jan 2019, 04:53
artiom01 wrote:
Archit3110

Shouldn't it be:

ax + by = c

by = -ax + c

y = -(a/b)x + c

?


y=mx+c
ax+by=c
ax-c=-by
question say : slope of line k is positive
a/bx-c/b=-y
so
a/b has to be +ve >0 ;
plot a graph you would get the relation on why a/b<0...
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Originally posted by Archit3110 on 20 Jan 2019, 00:44.
Last edited by Archit3110 on 20 Jan 2019, 04:53, edited 1 time in total.
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Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post 20 Jan 2019, 01:31
Archit3110 wrote:
artiom01 wrote:
Archit3110

Shouldn't it be:

ax + by = c

by = -ax + c

y = -(a/b)x + c

?


y=mx+c
ax+by=c
ax-c=-by
question say : slope of line k is positive
a/bx-c/b=-y
so
a/b has to be +ve >0 ;
plot a graph you would get the relation on why a/b>0...


But a/bx-c/b=-y is equal to y=-(a/b)x+c/b.
Therefore, as -(a/b) is the slope that has to positive, a/b has to be negative.
Attachments

File comment: a and b need to be one positive and one negative in order to make the slope of the line positive.
plot.jpg
plot.jpg [ 361.6 KiB | Viewed 421 times ]

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Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post 20 Jan 2019, 03:38
artiom01 wrote:
Archit3110 wrote:
artiom01 wrote:
Archit3110

Shouldn't it be:

ax + by = c

by = -ax + c

y = -(a/b)x + c

?


y=mx+c
ax+by=c
ax-c=-by
question say : slope of line k is positive
a/bx-c/b=-y
so
a/b has to be +ve >0 ;
plot a graph you would get the relation on why a/b>0...


But a/bx-c/b=-y is equal to y=-(a/b)x+c/b.
Therefore, as -(a/b) is the slope that has to positive, a/b has to be negative.


I agree with artiom01. Can anyone point out where I am going wrong?
Bunuel
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Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post 20 Jan 2019, 03:49
Hi Bunuel,

Could you please explain how the ans is A instead of B.
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Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

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New post 20 Jan 2019, 04:49
Bunuel wrote:
Line k is defined by the equation ax + by = c. If the slope of line k is positive, which of the following must be true?


A. a/b > 0

B. a/b < 0

C. a > 0

D. b > 0

E. a + b > 0


\(ax + by = c\);

\(y=-\frac{a}{b}*x+\frac{c}{b}\);

The slope is -a/b. We are told that it's positive, so \(-\frac{a}{b}>0\) --> \(\frac{a}{b}<0\).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Line k is defined by the equation ax + by = c. If the slope of line k   [#permalink] 20 Jan 2019, 04:49
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