Direct and inverse proportion

Last time

Before we start: last time, in Sequences and the nth term, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

More workers, less time

Six workers build a wall in ten days. How long would four workers take? Fewer workers means more days: that is inverse proportion. And if each metre of wall costs the same, the cost grows with the length: that is direct proportion. Today you set up the equation with the constant k, and use it, including squares and roots.

Direct proportion

Direct proportion means that as x grows, y grows by the same factor. Double x and y doubles. We write y is proportional to x, and turn it into an equation with a constant: y equals k times x. The constant k is called the constant of proportionality. It never changes.

The method

Step one: write the equation with k. Step two: use the given pair of values to find k. Step three: rewrite the equation with that k, and use it to find the unknown. For example: y is twelve when x is four. Then k is twelve over four, which is three. So y equals three x, and when x is seven, y is twenty-one.