Mathematics
Prove that infinitely many points lie on the line whose equation is y = 2x. (Hint : Consider the point (n, 2n) for any integer n.)
Mathematics Proofs
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Answer
Consider the point (n, 2n) for any integer n.
Given equation y = 2x ….(1)
Putting x = n and y = 2n in equation (1) we get :
⇒ 2n = 2(n)
⇒ 2n = 2n, which is always true.
So, (n, 2n) lies on equation (1).
Now for infinite values of n, we can obtain infinite points which lie on line whose equation is y = 2x.
Hence, proved that infinitely many points lie on the line whose equation is y = 2x.
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