Plotting the reciprocals of the same data points yields a "double- reciprocal" or Lineweaver-Burk plot. This provides a more precise way to determine Vmax and Km. Vmax is determined by the point where the line crosses the 1/Vi = 0 axis (so the [S] is infinite).  Note that the magnitude represented by the data points in this plot decrease from lower left to upper right.  Km equals Vmax times the slope of line. This is easily determined from the intercept on the X axis.