Inverse Proportion

In the previous post we basically defined direct proportion as what we do to x, we must also do to y. Specifically we said that if you double x, then we must double y to maintain the relationship as directly proportional. With inverse proportion when we double y we must halve x. The equation xy=k where k is the constant. For example suppose when x=3 y=20. If x is doubled to equal 6, y must be cut in half to 10 to maintain an inverse relationship. Using our equation xy=k we first solve for k--(3)20=60 so k=60; if we double x from 3 to 6 then we have 6y=60; y=10. So when x is doubled from 3 to 6, y is halved from 20 to 10. Simple as that.

Direct and Inverse Proportion

There is usually at least one question on the math section which requires the student to know either direct proportion or inverse proportion. Quite simply with direct proportion if x goes up y goes up in proportion. If x decreases, y decreases in proportion. Here is a helpful rule for Direct proportion using variables x and y can be thought of as y=xk where k is a constant. Cross multiply and you get a variation of this equation: y/x=k. For example if x=2 when y=4, then when x=4 then y=8. The constant k=2 so y will always be twice x. Simple enough? If x were to be reduced from 2 to 1 then y would still be twice x but in this case it would be reduced to 2. In our next entry the more difficult concept of inverse proportion will be tackled.