Recovering a reciprocal law from a straight line

Recovering a reciprocal law from a straight line

IP 3
6 marks

For \(x>0\), the graph of \(xy\) against \(x\) is a straight line with gradient \(2\) passing through \((1,5)\).

  1. Express \(y\) in terms of \(x\).[2]
  2. Find the value of \(x\) for which \(y=2.5\).[1]
  3. The straight line meets the vertical axis at \((0,3)\). Explain why this does not correspond to a point on the curve \(y\) against \(x\), and describe how \(y\) behaves as \(x\) becomes large.[3]

Solution:

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Answer:(a) \(y=2+\dfrac{3}{x}\) (b) \(x=6\) (c) \(y\) decreases towards \(2\)

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