Straight line, equation

Because of the hyperbolic shape of versus [S] plots, Vmax only be determined from an extrapolation of the asymptotic approach of v to some limiting value as [S] increases indefinitely (Figure 14.7) and is derived from that value of [S] giving v= V(nax/2. However, several rearrangements of the Michaelis-Menten equation transform it into a straight-line equation. The best known of these is the Lineweaver-Burk double-reciprocal plot ... 

Thus a plot of 1/i vs. l/fi1/2 would give a straight line, and the reaction rate constant, k, and diffusivity, D, can be respectively determined from the intercept, A, and the slope, B, of the straight line. Equations similar to those of the RDE may be also derived for other type electrochemical reaction using the procedures illustrated in Ref. [48, 50],... 

To find AG° at 1000°C, we simply plug jc =1273 K into the straight-line equation we developed above and solve for y (AG°). 

The integrated forms of equations (Table 1) can be rearranged in the form of a straight line equation y = mx + c. For example... 

COMPARISON OF CAROTENOID COMPOSITION (juG/G) OF LEAFY VEGETABLES OBTAINED BY ONE-POINT CALIBRATION, STRAIGHT LINE EQUATION AND RESPONSE FACTORS... 

Carotenoid Sample number One-point calibration Straight line equation... 

From the form of Equation 10, it is clear that a plot of cos 4 versus 1//Ysw will give a linear plot which will fit a straight-line equation... 

Constant a is the intersection point with the axis of ordinates and j8 is the slope of a straight-line equation ... 

A plot of logio Ed against 1/1) is almost rectilinear. Therefore, Ea may be determined by equating (EJ4.57) with the slope of the straight line. Equation 3.3 holds good for a number of explosives such as lead azide, cuprous azide, mercury fulminate, lead styphnate, barium styphnate and metal picrates and metal picramates etc. [25-30]. Thus, it appears that the determination of Ea gives a more complete picture concerning the heat sensitivity of explosives than ED or ET. 

All these statistics are available in Excel in the LINEST function. This gives an array output, and for fitting data to a straight line (equation 2.29) is created by following these steps ... 

As early as 1819, J. L. Gay Lussac proposed to represent the solubility S of potassium chloride in water at a temp. 0 by the formula /S=29-23+0-27380 grms. per 100 grms. of water. Since that time it has been customary to represent solubility curves by empirical formula of the type /S=a+ 0+d02+..., where a, l, c,d,.. . are constants whose numerical values are calculated from the experimental data. Equations of the type S=a- -bO represent straight lines, equations with more terms represent curved lines the solubility equation /S=d+60+c02 represents a portion of a paraboloid curve. The greater the number of terms used in the formula the greater is supposed to be the accuracy of the result. 

The nature of the relationship between P and drug activity depends on the range of P values obtained for the compounds used. If this range is small the results may be expressed as a straight line equation having the general form ... 

Profile parameter A r A2, Br By Axial sections of straight-line equations... 

The logarithm of the constants, calculated in the above way, changes linearly with the difference of [= TiOHj] and [= TiO densities. The constant in the straight line equation equals to the logarithm of the real ionization constant of the surface groups, whereas slope coefficient is proportional to the edl capacity. 

When true scale formation occurs, the overall heat-transfer coefficient may be related to the time the evaporator has been in operation by the straight-line equation ... 

The following form of the Arrhenius equation can be used to determine the activation energy for shifting of the glass transition temperature as well as for defining a straight line equation characterizing the shift as a function of frequency. 

In this equation, s is the slope of the straight-line equation between Ina as the dependent variable and ln(-AP) as the independent variable. By analogy with Equation Equation (7.62),... 

The previons equation is a straight-line equation between Int and InF. The equation is that of a straight line, so only two data points for Int and InF are required to calculate the constants m and K. Using the techniques of analytic geometry as applied to straight-line equations, the following equations are produced... 

Various equations derived earlier require the values of the kinetic constants Y, k, K and n. These constants are characteristics of a given waste and must be determined uniquely for that waste. This section will develop a method for obtaining these values from experimental data. This method is based on the fact that if an equation can be transformed into a straight-line equation, only two data points are needed to determine the values of the parameters. 

It is often possible to manipulate the mathematical model into the form of a straight-line equation. For example, the one compartment pharmacokinetic model after an IV bolus can be expressed as a differential equation or as an exponential equation as shown earlier. By taking the natural log of the exponential equation, Eq. (17) in the form of a straight line can be derived ... 

This graphic representation was not possible for the correlation data, since they cannot be directly compared with each other and have therefore been stated in figures. To the extent that data on comparative methods were available, these are shown. Patient comparisons based on a number of samples < 50 have been deliberately omitted since their statistical value may be doubtful. Exceptions from this rule were made only where no other data could be obtained. When measuring the enzyme activities it is necessary to consider the difference between methods in temperature, buffer, substrate and the effects of the isoenzymes. That is also why the ideal straight line equation (y = 1.00 x 0) can often not be achieved. In this regard it is only pointing out the statistical difference to another method. 

Straight line equation Correlation coefficient Number of samples compared Comparative method References... 

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