## Algebra 1

It is true that a quick check for direct or inverse variation is the see how x and y relate to one another (for instance, if x goes up, what does y do? If it goes up, it is direct variation; if it goes down, it is inverse variation). However, the k must remain the same in either case. So, if this were an inverse variation, k would remain constant. Consider the following values of x and y according to the pattern Pedro sees: (1,8), (2,6), (3,4, (4,2)). If this were truly an inverse variation, then $xy = k$, in which k is constant. Let's check: $1\times8 = 8$ $2\times6=12$ $3\times4 = 12$ $4\times2 = 8$ While some of our k's were the same, they should have been constant throughout, meaning this is not an inverse variation. Instead, this information follows the form of a line: $y=mx+b$.