Equation of a straight line

One of the most striking features of Fig. 2.10 is the change of slope. Let us begin our discussion of this feature by examining the slopes of the linear portions of these lines on either side of the break. Representing the equation of a straight line by y = ax -i- b, we can write an empirical equation for the phenomena shown in Fig. 2.10 as... 

This is the equation of a straight line, so rj and r2 can be evaluated fron the slope and intercept of an appropriate plot. 

What makes Eq. (8.87) especially important is that it is the equation of a straight line. It predicts that a plot of n/RTc2 versus C2 will be linear for dilute solutions and that the slope and intercept of the plot will have the following significance ... 

By taking the logarithm of both sides of Eq. (9.34), the Mark-Houwink equation is transformed into the equation of a straight line ... 

Assuming that concentration effects have been eliminated by extrapolating Kc2/Rg to C2 = 0 (subscript c = 0), we see that Eq. (10.89) is the equation of a straight line if (Kc2/Rg)(,=o plotted against sin (0/2). The characteristic parameters of the line have the following significance ... 

For design purposes it is useful to have a relationship between a a and Om, similar to those used for metals (e.g. the Soderberg and Goodman relationships). It is suggested that the equation of a straight line joining points W and Z in Fig. 2.76 would be best because it is simple and will give suitably conservative estimates for the permissible combinations of Oa and to produce failure in a pre-selected number of cycles. Such an equation would have the form... 

Symmetry 50. Intercepts 50. Asymptotes 50. Equations of Slope 51. Tangents 51. Equations of a Straight Line 52. Equations of a Circle 53. Equations of a Parabola 53. Equations of an Ellipse of Eccentricity e 54. Equations of a Hyperbola 55. Equations of Three-Dimensional Coordinate Systems 56. Equations of a Plane 56. Equations of a Line 57. Equations of Angles 57. Equation of a Sphere 57. Equation of an Ellipsoid 57. Equations of Hyperboloids and Paraboloids 58. Equation of an Elliptic Cone 59. Equation of an Elliptic Cylinder 59. 

Comparing this equation with the general equation of a straight line, y = b + mx (b = -intercept, m = slope)... 

Eq. (4-42) is the equation of a straight line between /(p) and /(q), whereas the right side is the curve traced out by the function as the argument varies in a straight line from p to q. Thus a convex upward function is one in which all chords lie below the function. 

The second form is statistically advantageous, but the first is amenable to linearized graphical analysis. It represents the equation of a straight line. A plot of (Y, — Too)-1 versus time will be a straight line with a slope from which k may be calculated k = slope x (Yq - Fx)/tA]o. Note that the bracketed quantity is the difference in y s (in spectrophotometry, the difference in molar absorptivities). Thus, k = slope X (yA - yP) = slope X (eA - p). 

This is the equation of a straight line. One constructs a plot of the incremental concentration differences against the logarithm of their ratios. The line gives k = -slope and k = intercept/r. Figure 2-11 presents this plot for the same data set points to 90 percent completion were used, with 375 s chosen for t. 

The use of the group of linear equations is more familiar, especially the equation of a straight line, y = mx + b. The procedure20 is this The experimenter defines the function... 

Lord Kelvin (1824-1907) was a great thermodynamicist whom we shall meet quite often in these pages. He noticed how the relationship in Equation (1.5) resembles the equation of a straight line, i.e. takes the form... 

Alternatively, the value of the true second-order rate constant may be obtained by treating Equation (8.36) as the equation of a straight line, with the form y = mx ... 

The general equation of a straight line relationship between an independent variable x and a dependent variable y is given by ... 

If Pi is constant, this is the equation of a straight line in the CliqH/Cliqi vs CliqH diagram, which is the foundation of widely used plots like Th/Ta vs Th aimed at identifying partial melting processes. These plots and alignment parameters were used... 

To calculate the concentrations of the unknowns and the control, use the equation of a straight line as follows, in which b is the y-intercept and m is the slope ... 

This is the equation of a straight line of slope Lm/Gm, which passes through the point (Xi, Y ). It may be seen by making a material balance over the whole column that the same line passes through the point (X2, Y2). This line, known as the operating line,... 

The Lineweaver-Burk plot uses the reciprocal of the Michaelis-Menten equation in the form of the equation of a straight line, y=mx + h, having the form shown in equation 2.3 ... 

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