Sketching lines for an algebraic law
Sketching lines for an algebraic law
Secondary 3
The variables \(x\) and \(y\), where \(x>0\), are related by \(y=3x-\dfrac{12}{x}\).
- Show that the graph of \(xy\) against \(x^2\) is a straight line. State its gradient and vertical intercept, and sketch it, marking where it meets the horizontal axis.
- The same law is now plotted as \(\dfrac{y}{x}\) against \(\dfrac{1}{x^2}\). State the gradient and vertical intercept of this line, and sketch it.
- The point \((9,\,q)\) lies on the line in part (a). Find \(q\) and the corresponding values of \(x\) and \(y\).
Solution:
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Answer:(a) gradient \(3\), intercept \(-12\), meets the horizontal axis at \((4,\,0)\) (b) gradient \(-12\), intercept \(3\) (c) \(q=15\), \(x=3\), \(y=5\)
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