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

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If a line passes through the point (3, 5) and has a positive  [#permalink]

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New post 17 Sep 2019, 10:36
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

47% (01:34) correct 53% (01:36) wrong based on 38 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 & II only
D. I, II & III
E. None of the above

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Re: If a line passes through the point (3, 5) and has a positive  [#permalink]

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New post 17 Sep 2019, 19:54
posiive slope lines are when x increases , y increases.
Here x <y hence when x =0, y will be less than 0
Hence A
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New post 18 Sep 2019, 06:36
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I would say none of the above. It completely depends on the gradient of the slope. For example if the gradient is 5 then the y intercept would be negative, and if the gradient was 1, then the y intercept would be positive
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New post 18 Sep 2019, 07:53
josephgc29 wrote:
I would say none of the above. It completely depends on the gradient of the slope. For example if the gradient is 5 then the y intercept would be negative, and if the gradient was 1, then the y intercept would be positive

With (E) as well for the exact same reasons , well explained, kudos added...
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Re: If a line passes through the point (3, 5) and has a positive  [#permalink]

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New post 03 Oct 2019, 21:37
josephgc29 wrote:
I would say none of the above. It completely depends on the gradient of the slope. For example if the gradient is 5 then the y intercept would be negative, and if the gradient was 1, then the y intercept would be positive


What is the difference between option D and E?
If, the gradient of the slope can take any value and thus, the intercept can take any (+,-,&0) then that choice is already present in option D.

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Re: If a line passes through the point (3, 5) and has a positive  [#permalink]

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New post 03 Oct 2019, 22:09
kshv wrote:
josephgc29 wrote:
I would say none of the above. It completely depends on the gradient of the slope. For example if the gradient is 5 then the y intercept would be negative, and if the gradient was 1, then the y intercept would be positive


What is the difference between option D and E?
If, the gradient of the slope can take any value and thus, the intercept can take any (+,-,&0) then that choice is already present in option D.

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Hi kshv,

The basic idea of the question is to see for what values of y-intercept will a line passing through (3, 5) have positive slope
as per the below figure, we can see all the values of y-intercepts less than 5 will satisfy the above condition
Image

So, the correct inequality MUST be c < 5

That's why option E is the answer

Think about this,
Can we say c must be less than 0 always? No right! Coz all values from 0 < c < 5 are left out. So, none of the options satisfy the condition 'MUST'

Hope i'm clear!
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Re: If a line passes through the point (3, 5) and has a positive  [#permalink]

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New post 03 Oct 2019, 22:21
Got it!!
Thank you so much.

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Re: If a line passes through the point (3, 5) and has a positive   [#permalink] 03 Oct 2019, 22:21
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