# Once more: direct and inverse variation.

It’s that time of year when my beginning algebra students are asked to consider how **y** varies as **x** varies. The major challenge of the year is helping these students believe that **x** and **y** are numbers…very powerful ones. That **y** varies directly with **x **is well expressed by the equation **y = kx**. That **y** varies inversely with **x**, **xy=k** or **y=k/x**. **k** represents the given constant of variation. Notice that no numerals appear in these simple equations. The symbols **x**, **y**, and **k** represent numbers and are thus useful, for they cover an infinity of cases. Each individual case is the source of numerals to replace the letters. In class we put numbers in the equations, and the students see the obvious. Take the numbers away; darkness returns. This is the struggle to guide a mind from arithmetic to algebra.