Straight line through two points

It is possible to draw a straight line through two points. The general equation of a straight line through two points Pj and P2 ( 2/ 2) can be 

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Once factor values are determined, the minimum number of experiments is governed by the number of coefficients in the model, but if only the minimum number of experiments is done, there is no way to check the model. An analogy is drawing a straight line through two points, which cannot fail, but measurement of a third point will allow a least squares lit with some indication of the status of the linear model. 

When you plot values of a variable z on a logarithmic axis and your plot yields a straight line through two points with coordinate values zi and zz, replace zz - Z with In (c2/ Ci) ( = In Z2 - In zi) in the formula for the slope. 

A STRAIGHT LINE THROUGH THE POINT SHOWN FOR A PARTICULAR EXPLOSIVE WILL INTERSECT THE TWO SCALES TO SHOW THE LOADING DENSITY RESULTING FROM ANY GIVEN loading PRESSURE. 

C Draw suitable lines through the points on your graph (note there are two parts to this graph so you will need to draw two straight lines through the points and extend them until they cross). 

The enthalpy of the liquid Zq is increased by the amount A/t, without any change of concentratioa In this way point 1 can be found. This point represents the enthalpy of the two-phase system with the phases vapor at x = 0 and liquid L with concentration Xj and pressure p, compare information on balances in previous chapters. The enthalpy of the solvent vapor is the stun of the enthalpy of the liquid, the heat of evaporation, and the enthalpy according to the superheated vapor. By this way the point Gj is fixed. According to the balances of energy and mass, the point of the liquid can be found as the intersection point of the straight line through the points Gj and 1 and the isobar curve p, = const. Therefore, the relationship... 

Similarly if Mw for the lower section is plotted at xwy then a straight line through this point intersects the two enthalpy curves at values that satisfy Eq. (7-27) and these straight lines give the relation between y and x i. 

The mathematical requirements for unique determination of the two slopes mi and ni2 are satisfied by these two measurements, provided that the second equation is not a linear combination of the first. In practice, however, because of experimental error, this is a minimum requirement and may be expected to yield the least reliable solution set for the system, just as establishing the slope of a straight line through the origin by one experimental point may be expected to yield the least reliable slope, inferior in this respect to the slope obtained from 2, 3, or p experimental points. In univariate problems, accepted practice dictates that we... 

To complete an approximate sketch of the titration curve, we draw separate straight lines through the two points before and after the equivalence point (Figure 9.35e). Finally, a smooth curve is drawn to connect the three straight-line segments (Figure 9.35f). 

Plot relative volatility (cq) and % desired recovery for LK and HK Draw a straight line through these two points. The non-key component points will also be on this straight line. 

The distribution of the other components can be readily determined by plotting the distribution of the keys against their relative volatility on log-log paper, and drawing a straight line through these two points. The method is illustrated in Example 11.6. 

Thus, the addition of two phases A and B is shown on the diagram by point C on the straight line joining the two phases, whilst the difference (A — B) is found by a point C on the extension of the line AB. If, as shown in Figure 11.24, a phase represented by C in the region between the dew-point and boiling-point curves is considered, then this phase will divide into two phases A and B at the ends of a tie line through the point C, so that ... 

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