text: Determining the parameters of the Michaelis–Menten equation typically involves running a series of enzyme assays at varying substrate concentrations , and measuring the initial reaction rates , i.e. the reaction rates are measured after a time period short enough for it to be assumed that the enzyme-substrate complex has formed, but that the substrate concentration remains almost constant, and so the equilibrium or quasi-steady-state approximation remain valid. By plotting reaction rate against concentration, and using nonlinear regression of the Michaelis–Menten equation with correct weighting based on known error distribution properties of the rates, the parameters may be obtained. 
  Before computing facilities to perform nonlinear regression became available, graphical methods involving linearisation of the equation were used. A number of these were proposed, including the Eadie–Hofstee plot of  against , the Hanes plot of  against , and the Lineweaver–Burk plot (also known as the double-reciprocal plot) of  against . Of these, the Hanes plot is the most accurate when  is subject to errors with uniform standard deviation. From the point of view of visualizaing the data the Eadie–Hofstee plot has an important property: the entire possible range of  values from  to  occupies a finite range of ordinate scale, making it impossible to choose axes that conceal a poor experimental design. 
  However, while useful for visualization, all three linear plots distort the error structure of the data and provide less precise estimates of  and  than correctly weighted non-linear regression. Assuming an error  on , an inverse representation leads to an error of  on  (Propagation of uncertainty), implying that linear regression of the double-reciprocal plot should include weights of . This was well understood by Lineweaver and Burk, who had consulted the eminent statistician W. Edwards Deming before analysing their data. Unlike nearly all workers since, Burk made an experimental study of the error distribution, finding it consistent with a uniform standard error in , before deciding on the appropriate weights. This aspect of the work of Lineweaver and Burk received virtually no attention at the time, and was subsequently forgotten.
  The direct linear plot is a graphical method in which the observations are represented by straight lines in parameter space, with axes  and : each line is drawn with an intercept of  on the  axis and  on the  axis. The point of intersection of the lines for different observations yields the values of  and .