Official Solution:

Which of the following points is not on the line \(y = 5x + 3\)?

A. \((\frac{1}{2}, \frac{11}{2})\)
B. \((\frac{1}{3}, \frac{14}{3})\)
C. \((\sqrt{8}, 3 + 10*\sqrt{2})\)
D. \((\sqrt{4}, 13)\)
E. \((\sqrt{2}, \frac{31}{3})\)

For \((\sqrt{2}, \frac{31}{3})\), the left hand side (LHS) becomes \(LHS=y=\frac{31}{3}=\text{rational}\) and \(RHS=5x + 3=5\sqrt{2}+3=\text{irrational}\) and since \(\text{rational} \ne \text{irrational}\), then line \(y=5x+3\) does not pass through point \((\sqrt{2}, \frac{31}{3})\).

Answer: E
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D does not work either

Hi,
D does fit in..
D. \((\sqrt{4},13)\)
y=5x+3..
substitute x= \(\sqrt{4}\) = 2 and y as 13..
13=5*2+3..
13=13..
OK
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi, I have the following doubts please clarify:
1. In D can't square root of 4 be + or -2?
.
2. I did not understand your explanation for E. Square root if 2 is approximately 1.41. so LHS is approximately 10.33. RHS = 5 * 1.41 + 3 which is approximately 10.08. Does this negligible difference be attributed to the reason that it does not lie on the line?

letter C, the value is for x or y?

First one is always X. In this case X= \sqrt{8}

Bunuel, chetan2u, thanks for your explanation. I have question on rational vs irrational point here. 31/3 also turns out to be irrational because 31/3 = 10.333333 which continues. So how 31/3 is rational.

Rational numbers are numbers that can be written in a fraction form. So they can be terminating decimal or can ALSO be non-terminating where the sequence repeats endlessly.. here too 31/3 =10.333333....
But in the right side √2 is non terminating and there is no sequence. Thus it is irrational

Hope it helps
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chetan2u , thanks this helps. Then can I assume any number in fraction form in given question is rational and any number like root 2 , root 3 for which square root is not integer is irrational number ?

yes, you can
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