Final answer:
Variables x and y are directly proportional if they increase or decrease together by a constant factor, described by y=kx. They are inversely proportional if one increases while the other decreases, described by y=k/x. The proportionality constant k can be found by dividing y by x for direct proportionality, and by multiplying y and x for inverse proportionality.
Step-by-step explanation:
To understand whether the sets of variables x and y are directly proportional or inversely proportional, we can look at their relationship. If two variables are directly proportional, when one variable increases, the other increases by a constant factor. This relationship can be described by the equation y = kx, where k is the constant of proportionality and represents how much y changes for a unit change in x. If we graph this relationship, we get a straight line passing through the origin.
In contrast, two variables are inversely proportional if an increase in one variable leads to a proportional decrease in the other. This relationship is expressed as y = k/x, where again k is a constant that stays the same as x and y change. Graphing inversely proportional variables results in a curve that never intersects the axes.
To find the constant of proportionality for a directly proportional relationship, divide y by x. For an inversely proportional relationship, multiply y and x to find k.