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fla162
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Which of the following equations represents a line on xy-plane that 15 Oct 2015, 18:21
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Difficulty:

65% (hard)

Question Stats:

55% (01:54) correct 45% (01:52) wrong based on 204 sessions

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Which of the following equations represents a line on xy-plane that includes exactly only one point P(Xp; Yp) with integer coordinates (Xp and Yp are both integer numbers)?

a) y= 2x
b) 2x-2y+1=0
c) y-5=3x
d) 2y-√2.x =0
e) 2y= x+2
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D
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ENGRTOMBA2018
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Which of the following equations represents a line on xy-plane that 15 Oct 2015, 19:07
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fla162
Which of the following equations represents a line on xy-plane that includes exactly only one point P(Xp; Yp) with integer coordinates (Xp and Yp are both integer numbers)?

a) y= 2x
b) 2x-2y+1=0
c) y-5=3x
d) 2y-√2.x =0
e) 2y= x+2
Show more


Easiest way is to do POE for the options to arrive at the correct answer. Incorrect options will either provide 0 integer coordinate pairs or will provide >1 integer coordinate pairs.

a) y= 2x , (0,0) m (1,2) etc. Eliminate
b) 2x-2y+1=0 --> y=x+0.5 , no integer coordinate pairs. Eliminate
c) y-5=3x ---> y=3x+5, (0,5), (1,8) etc. Eliminate
d) 2y-√2.x =0 ---> Only case possible = (0,0). Rest of them will be functions of \(\sqrt{2}\). Keep
e) 2y= x+2 ---> y=x/2+1 ---> (2,2) , (4,3) etc. Eliminate

Thus, D is the correct answer.

Hope this helps.
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Which of the following equations represents a line on xy-plane that 25 May 2020, 11:09
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ENGRTOMBA2018
fla162
Which of the following equations represents a line on xy-plane that includes exactly only one point P(Xp; Yp) with integer coordinates (Xp and Yp are both integer numbers)?

a) y= 2x
b) 2x-2y+1=0
c) y-5=3x
d) 2y-√2.x =0
e) 2y= x+2


Easiest way is to do POE for the options to arrive at the correct answer. Incorrect options will either provide 0 integer coordinate pairs or will provide >1 integer coordinate pairs.

a) y= 2x , (0,0) m (1,2) etc. Eliminate
b) 2x-2y+1=0 --> y=x+0.5 , no integer coordinate pairs. Eliminate
c) y-5=3x ---> y=3x+5, (0,5), (1,8) etc. Eliminate
d) 2y-√2.x =0 ---> Only case possible = (0,0). Rest of them will be functions of \(\sqrt{2}\). Keep
e) 2y= x+2 ---> y=x/2+1 ---> (2,2) , (4,3) etc. Eliminate

Thus, D is the correct answer.

Hope this helps.
Show more

In option d, if I write it as :
y=(√2*x)/2
>> y=x/√2

Then taking 'x' as 8 (which can be written as √2*2), I get the value of 'y' as 2

This case also satisfies the criteria and not just (0,0).

Do u agree or am I missing something?
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Which of the following equations represents a line on xy-plane that 25 May 2020, 11:29
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riagarg07
ENGRTOMBA2018
fla162
Which of the following equations represents a line on xy-plane that includes exactly only one point P(Xp; Yp) with integer coordinates (Xp and Yp are both integer numbers)?

a) y= 2x
b) 2x-2y+1=0
c) y-5=3x
d) 2y-√2.x =0
e) 2y= x+2


Easiest way is to do POE for the options to arrive at the correct answer. Incorrect options will either provide 0 integer coordinate pairs or will provide >1 integer coordinate pairs.

a) y= 2x , (0,0) m (1,2) etc. Eliminate
b) 2x-2y+1=0 --> y=x+0.5 , no integer coordinate pairs. Eliminate
c) y-5=3x ---> y=3x+5, (0,5), (1,8) etc. Eliminate
d) 2y-√2.x =0 ---> Only case possible = (0,0). Rest of them will be functions of \(\sqrt{2}\). Keep
e) 2y= x+2 ---> y=x/2+1 ---> (2,2) , (4,3) etc. Eliminate

Thus, D is the correct answer.

Hope this helps.

In option d, if I write it as :
y=(√2*x)/2
>> y=x/√2

Then taking 'x' as 8 (which can be written as √2*2), I get the value of 'y' as 2

This case also satisfies the criteria and not just (0,0).

Do u agree or am I missing something?
Show more

Hi riagarg07

8 cannot be written as √2*2.

8 is actually (√2*2)^2 so if x=8, y=8/√2 or 4√2

Hope this helps

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