Inverse Variation

Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 47 of 54.

48 sweets are shared equally among some children. With 3 children each gets 16; with 6 children each gets 8. Double the children and each share halves: the share varies inversely with the number of children.

In symbols, y = k/x, with k fixed. Here y = 48/x, and the product xy is always 48: 3 times 16, and 6 times 8. To use the rule, put x in: with 6 children, y = 48/6, which is 8.

Compare the two kinds. In direct variation y over x stays fixed, and with a positive k, y grows with x. In inverse variation x times y stays fixed, and with a positive k, y shrinks as x grows. x can never be 0: nothing is shared among no children.

Challenge

y varies inversely with x, and y is 4 when x is 9. Find y when x is 6. On the blank board, first find the constant k on a k = ... line, then write y = ... with that k.