Unlike the graph of direct variation, the graph of inverse variation is not linear. Rather, it is a hyperbola:
Note that the lines never cross the axes -- they get closer and closer to x = 0 and y = 0, but x and y never equal zero.
To graph an inverse variation, make a data table and plot points. Then connect the points with a smooth (not straight) curve. There should be two curves -- one in the first quadrant (where both x and y are positive) and one in the third quadrant (where both x and y are negative). The result should be qualitatively similar to the graph of xy = 1 above.
To calculate the constant of variation from a graph of inverse variation, simply pick a point and multiply its two coordinates.