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If a line passes through the point (3, 5) and has a positive slope

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Bunuel
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If a line passes through the point (3, 5) and has a positive slope [#permalink] New post   09 Feb 2023, 11:25
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60% (01:14) correct 40% (01:33) wrong based on 83 sessions
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If a line passes through the point (3, 5) and has a positive slope, then which of the following must be true about the y-intercept (c) of the line ?

I. c < 0
II. c = 0
III. c > 0

A. I only
B. II only
C. I and II only
D. I, II and III
E. None of the above
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E
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stne
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If a line passes through the point (3, 5) and has a positive slope [#permalink] New post   15 Feb 2023, 10:32
Bunuel wrote:
If a line passes through the point (3, 5) and has a positive slope, then which of the following must be true about the y-intercept (c) of the line ?

I. c < 0
II. c = 0
III. c > 0

A. I only
B. II only
C. I and II only
D. I, II and III
E. None of the above

A line has a positive slope when it moves from the 3rd Quadrant to the 1st quadrant
Please refer to the attached graph. The point shown is \((3,5)\)
Attachment:
GMAT slope 1.jpg
GMAT slope 1.jpg [ 12.52 KiB | Viewed 1378 times ]


We can see that the \(y\)-intercept can satisfy all of the three options.

I. \(c < 0,\hspace{2mm} \) need not necessarily be true as \(c=0,\) e.g. line \(2\) and \(c>0\) e.g.line \(1\) are also possible.
II. \(c = 0,\hspace{1mm} \) need not necessarily be true as \(c >0,\) e.g. line \(1\) and \(c<0\) e.g.line \(3\) are also possible.
III. \(c>0,\hspace{0mm} \) need not necessarily be true as \(c =0,\) e.g. line \(2\) and \(c< 0\) e.g.line \(3\) are also possible.

Ans E

Hope it's clear

Bunuel wrote:
Test....................
It works for me.
What type of attachment are you trying to upload?

Thank you, seems there was an issue with my external HDD. Saved image to system HDD and was able to upload.
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lowkyprofessional
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Re: If a line passes through the point (3, 5) and has a positive slope [#permalink] New post   25 Sep 2023, 20:37
stne wrote:
Bunuel wrote:
If a line passes through the point (3, 5) and has a positive slope, then which of the following must be true about the y-intercept (c) of the line ?

I. c < 0
II. c = 0
III. c > 0

A. I only
B. II only
C. I and II only
D. I, II and III
E. None of the above

A line has a positive slope when it moves from the 3rd Quadrant to the 1st quadrant
Please refer to the attached graph. The point shown is \((3,5)\)
Attachment:
GMAT slope 1.jpg


We can see that the \(y\)-intercept can satisfy all of the three options.

I. \(c < 0,\hspace{2mm} \) need not necessarily be true as \(c=0,\) e.g. line \(2\) and \(c>0\) e.g.line \(1\) are also possible.
II. \(c = 0,\hspace{1mm} \) need not necessarily be true as \(c >0,\) e.g. line \(1\) and \(c<0\) e.g.line \(3\) are also possible.
III. \(c>0,\hspace{0mm} \) need not necessarily be true as \(c =0,\) e.g. line \(2\) and \(c< 0\) e.g.line \(3\) are also possible.

Ans E

Hope it's clear

Bunuel wrote:
Test....................
It works for me.
What type of attachment are you trying to upload?

Thank you, seems there was an issue with my external HDD. Saved image to system HDD and was able to upload.



Since all three are possible why can't the answer choice be option D?
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Bunuel
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Re: If a line passes through the point (3, 5) and has a positive slope [#permalink] New post   26 Sep 2023, 00:23
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lowkyprofessional wrote:
stne wrote:
Bunuel wrote:
If a line passes through the point (3, 5) and has a positive slope, then which of the following must be true about the y-intercept (c) of the line ?

I. c < 0
II. c = 0
III. c > 0

A. I only
B. II only
C. I and II only
D. I, II and III
E. None of the above

A line has a positive slope when it moves from the 3rd Quadrant to the 1st quadrant
Please refer to the attached graph. The point shown is \((3,5)\)
Attachment:
GMAT slope 1.jpg


We can see that the \(y\)-intercept can satisfy all of the three options.

I. \(c < 0,\hspace{2mm} \) need not necessarily be true as \(c=0,\) e.g. line \(2\) and \(c>0\) e.g.line \(1\) are also possible.
II. \(c = 0,\hspace{1mm} \) need not necessarily be true as \(c >0,\) e.g. line \(1\) and \(c<0\) e.g.line \(3\) are also possible.
III. \(c>0,\hspace{0mm} \) need not necessarily be true as \(c =0,\) e.g. line \(2\) and \(c< 0\) e.g.line \(3\) are also possible.

Ans E

Hope it's clear

Bunuel wrote:
Test....................
It works for me.
What type of attachment are you trying to upload?

Thank you, seems there was an issue with my external HDD. Saved image to system HDD and was able to upload.



Since all three are possible why can't the answer choice be option D?


This is because the question asks "which of the following MUST be true," not "which of the following COULD be true," and while each option could be true, none of them is necessarily true.
GMAT Club Bot
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Re: If a line passes through the point (3, 5) and has a positive slope [#permalink]
26 Sep 2023, 00:23
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