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# Which of the lines in the figure above contains only points (x,y) with

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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
Can some one please elaborate a little

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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
Can someone please explain this in brief!
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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
BrentGMATPrepNow wrote:
Bunuel wrote:

Which of the lines in the figure above contains only points (x,y) with x = y?

(A) A
(B) B
(C) C
(D) D
(E) E

Attachment:
Quant9.jpg

GIVEN: equation of line is x = y

Anther approach is to rewrite equation in slope y-intercept form y = mx + b, where m = slope of the line, and b = the y-intercept
Take the equation x = y and rewrite as: y = 1x + 0

Aha, so the line's slope is 1, and its y-intercept is 0
Line D is the only line with a positive slope, AND line D also has a y-intercept of 0

Hi BrentGMATPrepNow, in x = y, how did you get from y = mx + b > y = 1x + 0? As I got y = my+b. Also not quite sure how did b become 0 here? Thanks Brent
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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
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Kimberly77 wrote:
BrentGMATPrepNow wrote:
Bunuel wrote:

Which of the lines in the figure above contains only points (x,y) with x = y?

(A) A
(B) B
(C) C
(D) D
(E) E

Attachment:
Quant9.jpg

GIVEN: equation of line is x = y

Anther approach is to rewrite equation in slope y-intercept form y = mx + b, where m = slope of the line, and b = the y-intercept
Take the equation x = y and rewrite as: y = 1x + 0

Aha, so the line's slope is 1, and its y-intercept is 0
Line D is the only line with a positive slope, AND line D also has a y-intercept of 0

Hi BrentGMATPrepNow, in x = y, how did you get from y = mx + b > y = 1x + 0? As I got y = my+b. Also not quite sure how did b become 0 here? Thanks Brent

Here are three important properties of numbers:

Property #1): If x = y, then we can also say that y = x
Example: Since 2 + 3 = 5, we can also say that 5 = 2 + 3

Property #2): x = 1x
Example: 5 = (1)(5)

Property #3): x = x + 0
Example: 3 = 3 + 0

so...........

Given: x = y
From property #1, we can say: y = x
From property #2, we can say: y = 1x
From property #3, we can say: y = 1x + 0

When we compare the equation y = 1x + 0 to the equation y = mx + b, we can see that m = 1 and b = 0

Does that help?
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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
Bunuel wrote:

Which of the lines in the figure above contains only points (x,y) with x = y?

(A) A
(B) B
(C) C
(D) D
(E) E

Attachment:
Quant9.jpg

Line D Intersects, Line C & Line E at (3,3) and Origin at (0,0), Answer must be (D)
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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
Brilliant thanks BrentGMATPrepNow. Great explanation always...I see your innovative and simple approach now. Perfectly make sense.
I was thinking of x=y which I see that line C & E both have (x,y) of (3,3) here. Where line D has (x,y) of (0,3). What went wrong with this reasoning here? Thanks Brent
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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
Top Contributor
Kimberly77 wrote:
Brilliant thanks BrentGMATPrepNow. Great explanation always...I see your innovative and simple approach now. Perfectly make sense.
I was thinking of x=y which I see that line C & E both have (x,y) of (3,3) here. Where line D has (x,y) of (0,3). What went wrong with this reasoning here? Thanks Brent

I think you mean that lines C, D and E all pass through (2,2).
However, only line D passes through (3,3)

Also noticed that line D does NOT pass-through the point (0, 3)
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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
BrentGMATPrepNow wrote:
Kimberly77 wrote:
Brilliant thanks BrentGMATPrepNow. Great explanation always...I see your innovative and simple approach now. Perfectly make sense.
I was thinking of x=y which I see that line C & E both have (x,y) of (3,3) here. Where line D has (x,y) of (0,3). What went wrong with this reasoning here? Thanks Brent

I think you mean that lines C, D and E all pass through (2,2).
However, only line D passes through (3,3)

Also noticed that line D does NOT pass-through the point (0, 3)

Ah you're right BrentGMATPrepNow and my bad, mistaken lines C & E here by looking at 3 .
With line D, Could we say it pass (3,3) (4,4) (5,5) so on here (as only then I can see it pass through 3,3) and it also pass through origin (0,0) in the middle? Thanks Brent
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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
Top Contributor
Kimberly77 wrote:
BrentGMATPrepNow wrote:
Kimberly77 wrote:
Brilliant thanks BrentGMATPrepNow. Great explanation always...I see your innovative and simple approach now. Perfectly make sense.
I was thinking of x=y which I see that line C & E both have (x,y) of (3,3) here. Where line D has (x,y) of (0,3). What went wrong with this reasoning here? Thanks Brent

I think you mean that lines C, D and E all pass through (2,2).
However, only line D passes through (3,3)

Also noticed that line D does NOT pass-through the point (0, 3)

Ah you're right BrentGMATPrepNow and my bad, mistaken lines C & E here by looking at 3 .
With line D, Could we say it pass (3,3) (4,4) (5,5) so on here (as only then I can see it pass through 3,3) and it also pass through origin (0,0) in the middle? Thanks Brent

Yes, we can say that line D pass through all those points
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Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
Awesome...thanks BrentGMATPrepNow for confirmation.
Re: Which of the lines in the figure above contains only points (x,y) with [#permalink]
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