The difference between direct and an inverse proportion is simple to explain by using equations. While the equation for direct proportions is y = kx, the equation for inverse proportions is y = k/x. In these equations, k is a constant, and x and y are the variables.
In a direct proportion, as the variable X increases as does the variable Y, and K is the constant of proportionality that relates these two values. An example of this type of relationship is a person gets paid $10 an hour for a job. If the person works five hours, then he gets paid $50. In this direct proportion, k = $10, x = 5 and y = $50. The equation is y = $10x. From this equation, one can see that the more hours worked by a person, the higher the amount of pay. If one writes the equation as k = y/x, then one sees that the ratio y/x remains the same.
In an inverse proportion, the two variables are inversely proportional to one another. One can write this equation as y = k/x, where K is the constant of proportionality that relates the two variable. In this equation as X increases, Y decreases. If k = 1 and x = 2, then y = 1/2. An example of this type of problem is that if two people work on the same job, then it takes half the time then if it were only one person. On can also rewrite the equation y = k/x as yx = k. This means that the product of the two variables must remain the same.