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

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Bunuel
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Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   17 Jan 2019, 02:47
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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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B
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Archit3110
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Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   Updated on: 20 Jan 2019, 05:54
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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

Originally posted by Archit3110 on 17 Jan 2019, 07:16.
Last edited by Archit3110 on 20 Jan 2019, 05:54, edited 3 times in total.
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LevanKhukhunashvili
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Re: Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   18 Jan 2019, 05:51
Got confused

Archit3110
Can you explain this part?


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

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Archit3110
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Re: Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   18 Jan 2019, 06:05
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LevanKhukhunashvili wrote:
Got confused

Archit3110
Can you explain this part?


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

Regards
L

LevanKhukhunashvili

Solution attached

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IMG_20190118_183326967.jpg
IMG_20190118_183326967.jpg [ 3.49 MiB | Viewed 3478 times ]

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Re: Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   20 Jan 2019, 01:28
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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] New post   Updated on: 20 Jan 2019, 05:53
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...

Originally posted by Archit3110 on 20 Jan 2019, 01:44.
Last edited by Archit3110 on 20 Jan 2019, 05:53, edited 1 time in total.
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artiom01
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Re: Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   20 Jan 2019, 02:31
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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.
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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
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Re: Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   20 Jan 2019, 04:38
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?
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Re: Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   20 Jan 2019, 04:49
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] New post   20 Jan 2019, 05:49
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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.
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Re: Line k is defined by the equation ax + by = c. If the slope of line k [#permalink] New post   12 Dec 2020, 03:10
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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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