Slope intercept equation

SLOPE-INTERCEPT EQUATION SLOPE REPLOTS (or, Slope Secondary Replots)... 

It is frequently very helpful to plot data. The data is often easier to analyze when it is presented so as to obtain a linear relationship. One of the most useful forms of graphing data is to use the slope intercept equation for a straight line ... 

Because h is the intercept and m is the slope, the equation of the straight line is equivalent to... 

From the quotient between the inverted slope of Equation 43 and the intercept of Equation 28. e Cyclohexane/benzene ratio of 99 1. 

The intercept term C Ar/ Ar)o, which accounts for igneous, metamorphic, or atmospheric sources, is regarded as the excess contribution present at time = 0, whereas the second term is the radiogenic component accumulating in the various minerals of the isochron by decay of If all the minerals used to construct the isochron underwent the same geologic history and the same sort of contamination by excess " Ar, the slope of equation 11.100 would have a precise chronological... 

Its obviously linear form lends itself to analysis by the plotting and regression techniques introduced previously for equations 7 and 11. For homologous series in which the enthalpy of reaction is more-or-less constant for all members, the slope of equation 36 is close to 1 and the y-intercept, AHIxa , is approximately equal to the mean experimental enthalpy of reaction, AHrxa. The direction of deviation of the slope from unity for any carbonyl/product pair indicates whether the hypothetical reaction enthalpy will increase or decrease for the series. Inclusion of the enthalpies of formation of the appropriate XY reagent (or a combination of reagents and/or by-products) shows whether the reaction is actually endo- or exothermic. Some results are summarized in Table 6. 

Also important to the validation process of QSARs is vertical validation. In this instance, quantitatively similar QSARs are developed with similar descriptors but using data for a different toxic endpoint. For example, the investigation of Karabunarliev et al. (1996b) modeled acute aquatic toxicity data for the fathead minnow Pimephales promelas. The compounds considered in the analysis were confined to substituted benzenes, and descriptors limited to log Kow and Amjx. The fish toxicity QSAR (log [LQ,]-1 = 0.62 log K, + 9.17 A - 3.21 n = 122 R2 = 0.83 i = 0.16 F = 292) of Karabunarliev et al. (1996b) was very similar in terms of slope, intercept, and statistical fit to the QSAR presented in Equation 12.2. The fact that different endpoints provide very similar QSARs indicates that the QSAR is valid across protocols. This shows the universality of the model. 

Notice that this last equation is in slope intercept form (y = mx+b) if we substitute log y for y and log x for x. Thus if we graph log y on the vertical axis and log x on the horizontal axis, the result will be a straight line. Furthermore the slope of this line will be n and the vertical intercept (i.e. the intercept on the log y axis) will be log a. 

Answer Because you are solving for the concentration of N205 at time t, it is probably best to use the slope-intercept version of the formula. This equation will be set up as follows ... 

Notice again that this is written in the slope-intercept format, where the slope of the line is k once again. The differences between the equations and graphs of a second-order reaction and a first-order reaction are frequently a topic on the AP test in some form or another. 

To derive the Lineweaver-Burk equations, we proceed by simply taking the reciprocals of each side of the equations expressing v0 as a function of [S]0 in Table 9-1. The corresponding graphs of l/u0 versus l/[S]o have varying slopes, intercepts, or both as [I] is varied. Pure noncompetitive inhibition shows lines... 

We might have thought, because the experimental AH°f methylene increment slopes are different for the two series while the IE methylene increment slopes are identical, that the methylene increment slopes calculated from ST would be non-identical. The slopes from the linear regressions of ST vs. n for the two series are just within each other s standard errors. This statistical sameness of all slopes [16] is an artifact because, as it must, combining the IE and ST methylene increments for each homologous series reproduces the non-identical slopes from equation 3 for the compounds of relevant nc. From the slope/intercept constants generated above and eq. 6, the calculated enthalpy of formation (hartree) for an alkane with nc = 4-6 is... 

The standard errors reported for the constants in the two equations above were calculated as the root mean square of the component standard errors and this propagation of uncertainty in the combined equations causes the slopes to barely overlap, whereas there is no overlap of the slopes calculated from eq. 3. We cannot hope to use these equations to calculate accurate enthalpies of formation for alkanes or alcohols with nc > 6 for the same reason we cannot use eq. 3 and the same restricted data range the calculated results do not reproduce the experimental results due to the sensitivity of the calculation to the slope/intercept. 

Linear plots of Fj/( — Fq) vs. have been obtained for a large variety of organic solutes and have been utilized for the evaluation of the substrate-micelle association constant, K, from the slope, intercept, and equation (15) (Herries et al., 1964 Dunlap and Cordes, 1968 Romsted and Cordes 1968). Fig. 5 illustrates a typical plot of this type for the elution of p-nitrophenol in sodium dodecyl sulfate solution. 

The vertical and horizontal axes must be labeled with the appropriate symbols or words and the units indicated in parentheses for example, T (°C), t(s), A (cm ), density (g cm ). Often it is appropriate to add a smooth curve representing an equation arising from theory. The equation itself (if simple) or the number by which it is designated in the text must be given beside the theory crave. It is good practice to indicate directly on the figrrre the ntrmerical values of any slopes, intercepts, areas, maxima, or other featrrres that are important in the calcrrlatiorrs. 

The slope of Equation 18 is the mean value for 15 different sets of drugs (ionic and nonionic) causing hemolysis. The intercept is the mean value from seven sets of neutral drugs causing hemolysis. 

The determination of the specific cake and medium resistance can be extracted from the slope and axis intercept of the graph for the cake formation using Equation 6. ft can be seen that, the inverse slope of Equation 6, 1/Kc, can be taken as the indication of the filtration rate, dVi/dt. When 1/Kc increases the filtration rate increases (4). 

This is an interesting situation since the triplet emission of biacetyl is sensitized by the triplet state of benzene and yet slope/intercept is the same for (77) as for (75), and the latter is the equation for the singlet state of benzene. 

The resulting KA estimate for oxotremorine according to Equation 5.13 (KA = slope/intercept) is 8.1 pM. 

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