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

Question

https://gmatclub.com/forum/download/file.php?id=44905 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 Quant9.jpg

doomedcat · Answer

x=y=3
Line D passes through this point hence D

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BrentGMATPrepNow · Answer

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

Answer: D

Rajashree123 · Answer

Can some one please elaborate a little

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PrachiMaloo · Answer

Can someone please explain this in brief!

Kimberly77 · Answer

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

BrentGMATPrepNow · Answer

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?

Abhishek009 · Answer

Line D Intersects, Line C & Line E at (3,3) and Origin at (0,0), Answer must be (D)

Kimberly77 · Answer

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

BrentGMATPrepNow · Answer

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)

Kimberly77 · Answer

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

BrentGMATPrepNow · Answer

Yes, we can say that line D pass through all those points

Kimberly77 · Answer

Awesome...thanks  BrentGMATPrepNow  for confirmation.

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

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