The Michaelis constant, K_{m}, is a parameter in the MichaelisMenten equation. K_{m} is equal to the substrate concentration where the corresponding reaction rate is ½ • V_{max}. An enzyme with a low K_{m}, therefore, achieves its halfmaximal velocity at a low substrate concentration, while an enzyme with a high K_{m} needs high substrate concentrations to achieve this velocity. It has been experimentally shown, that K_{m} of an enzyme is usually close to the cellular concentration of its substrate. For an enzymatic reaction involving 2 steps, where the second step is ratelimiting, K_{m} is approximately equal to the dissociation constant of the ES complex. In this case, a low K_{m} implies a high affinity for the substrate; however, this interpretation of K_{m} is only valid for a few enzymes [1]. K m, is a parameter in the MichaelisMenten equation. K m is equal to the substrate concentration where the corresponding reaction rate is half of V max. An enzyme with a low K m, therefore, achieves its halfmaximal velocity at a low substrate concentration, while an enzyme with a high K m needs high substrate concentrations to achieve this velocity. It has been experimentally shown, that K m of an enzyme is usually close to the cellular concentration of its substrate. For an enzymatic reaction involving 2 steps, where the second step is ratelimiting, K m is approximately equal to the dissociation constant of the E S complex. In this case, a low K m implies a high affinity for the substrate; however, this interpretation of K m is only valid for a few enzymes.
Figure 1: Figure 1a; MichaelisMenten equation fitted to a plot of initial rates against substrate concentration. When the substrate concentration equals K_{m}, the reaction rate is ½*V_{max}. K m, the reaction rate is half of V max. Figure 1b; An illustration of the LineweaverBurk equation fitted to a doublereciprocal transformation of an enzyme kinetic dataset.
The LineweaverBurk equation
Several methods for determining K_{m} exist. The most direct method is to plot V_{0} against [S] k m exist. The most direct method is to plot v 0 against the substrate concentration and use curve fitting software to fit the MichaelisMenten equation directly. However, certain transformations allow determination via linear regression, and these transformations are also useful when analyzing enzyme inhibition. Several transformations are possible; however, a simple one is obtained by taking the reciprocal on both sides of the MichaelisMenten equation. This leads to the following expression, called the LineweaverBurk equation:
1/V_{0} = 1/V_{max} + K_{m}/V_{max} • 1/[S] the reciprocal of V 0 equals the reciprocal of V max plus k m divided by V max times the reciprocal of the substrate's concentration
This equation shows, that a plot of 1/V_{0} against 1/[S] should give a plot that can be fitted by a straight line with the yintercept 1/V_{max} and slope K_{m}/V_{max}. Thus, K_{m} can be obtained using linear regression. Figure 1b shows an illustration of how to interpret the slope and intersects on a LineweaverBurk plot. [1] This equation shows, that a plot of the reciprocal of V 0 against the reciprocal of the substrate's concentration should give a plot that can be fitted by a straight line with the yintercept reciprocal of V max and slope k m divided by V max. Thus, K m can be obtained using linear regression. Figure 1b shows an illustration of how to interpret the slope and intersects on a LineweaverBurk plot.
Notable, the LineweaverBurk transformation is not the only option. For example, a plot of [S]/V_{0} against [S] (a Hanes–Woolf plot) will also result in a straight line [2]. the substrate's concentration divided by V 0 against the substrate's concentration, a Hanes–Woolf plot, will also result in a straight line. However, in this case, we will use the LineweaverBurk transformation.
References

Lehninger, Albert L.; Nelson, David L.; Cox, Michael M. (2008). Principles of Biochemistry (5th ed.). New York, NY: W.H. Freeman and Company. ISBN 9780716771081.

Atkins, G.L. and Nimmo, I.A. (1975) A comparison of seven methods for fitting the MichaelisMenten equation. Biochem. J. 149, 775777.
Initial reaction rate
V_{max}
Theory overview